KILLED proof of input_Fist6FNT1t.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 10 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 362 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 143 ms] (22) typed CpxTrs (23) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (24) CpxWeightedTrs (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTypedWeightedTrs (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) InliningProof [UPPER BOUND(ID), 56 ms] (34) CpxRNTS (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRNTS (37) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 419 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 100 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 261 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) CompletionProof [UPPER BOUND(ID), 0 ms] (54) CpxTypedWeightedCompleteTrs (55) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (58) CdtProblem (59) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CpxRelTRS (69) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (70) CpxTRS (71) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CpxWeightedTrs (73) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CpxTypedWeightedTrs (75) CompletionProof [UPPER BOUND(ID), 0 ms] (76) CpxTypedWeightedCompleteTrs (77) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CpxTypedWeightedCompleteTrs (79) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (80) CpxRNTS (81) InliningProof [UPPER BOUND(ID), 284 ms] (82) CpxRNTS (83) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CpxRNTS (85) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CpxRNTS (87) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (88) CpxRNTS (89) IntTrsBoundProof [UPPER BOUND(ID), 118 ms] (90) CpxRNTS (91) IntTrsBoundProof [UPPER BOUND(ID), 73 ms] (92) CpxRNTS (93) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (94) CpxRNTS (95) IntTrsBoundProof [UPPER BOUND(ID), 502 ms] (96) CpxRNTS (97) IntTrsBoundProof [UPPER BOUND(ID), 64 ms] (98) CpxRNTS (99) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (100) CpxRNTS (101) IntTrsBoundProof [UPPER BOUND(ID), 221 ms] (102) CpxRNTS (103) IntTrsBoundProof [UPPER BOUND(ID), 12 ms] (104) CpxRNTS (105) ResultPropagationProof [UPPER BOUND(ID), 3 ms] (106) CpxRNTS (107) CompletionProof [UPPER BOUND(ID), 0 ms] (108) CpxTypedWeightedCompleteTrs (109) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (110) CpxRNTS (111) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 141 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 51 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 184 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 556 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 186 ms] (172) CdtProblem (173) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 240 ms] (174) CdtProblem (175) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 799 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 438 ms] (178) CdtProblem (179) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 1104 ms] (180) CdtProblem (181) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 364 ms] (182) CdtProblem (183) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 433 ms] (184) 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: fib(N) -> sel(N, fib1(s(0), s(0))) fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) fib1(X1, X2) -> n__fib1(X1, X2) add(X1, X2) -> n__add(X1, X2) activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) activate(n__add(X1, X2)) -> add(activate(X1), activate(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: fib(N) -> sel(N, fib1(s(0'), s(0'))) fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) add(0', X) -> X add(s(X), Y) -> s(add(X, Y)) sel(0', cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) fib1(X1, X2) -> n__fib1(X1, X2) add(X1, X2) -> n__add(X1, X2) activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) activate(n__add(X1, X2)) -> add(activate(X1), activate(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: fib(N) -> sel(N, fib1(s(0), s(0))) fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) fib1(X1, X2) -> n__fib1(X1, X2) add(X1, X2) -> n__add(X1, X2) activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: fib(z0) -> sel(z0, fib1(s(0), s(0))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0, z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0, cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 S tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0, z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0, cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 K tuples:none Defined Rule Symbols: fib_1, fib1_2, add_2, sel_2, activate_1 Defined Pair Symbols: FIB_1, FIB1_2, ADD_2, SEL_2, ACTIVATE_1 Compound Symbols: c_2, c1, c2, c3, c4_1, c5, c6, c7_2, c8_2, c9_2, c10_2, c11_2, c12 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0, z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0, cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 The (relative) TRS S consists of the following rules: fib(z0) -> sel(z0, fib1(s(0), s(0))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: FIB(z0) -> c(SEL(z0, fib1(s(0'), s(0'))), FIB1(s(0'), s(0'))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0', z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0', cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 The (relative) TRS S consists of the following rules: fib(z0) -> sel(z0, fib1(s(0'), s(0'))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0', z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0', cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: FIB(z0) -> c(SEL(z0, fib1(s(0'), s(0'))), FIB1(s(0'), s(0'))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0', z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0', cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 fib(z0) -> sel(z0, fib1(s(0'), s(0'))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0', z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0', cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Types: FIB :: 0':s:cons:n__fib1:n__add -> c c :: c6:c7 -> c1:c2 -> c SEL :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c6:c7 fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add s :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add 0' :: 0':s:cons:n__fib1:n__add FIB1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c1:c2 c1 :: c1:c2 c2 :: c1:c2 ADD :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c3:c4:c5 c3 :: c3:c4:c5 c4 :: c3:c4:c5 -> c3:c4:c5 c5 :: c3:c4:c5 cons :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c6 :: c6:c7 c7 :: c6:c7 -> c8:c9:c10:c11:c12 -> c6:c7 activate :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add ACTIVATE :: 0':s:cons:n__fib1:n__add -> c8:c9:c10:c11:c12 n__fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c8 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c9 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 n__add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c10 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c11 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c12 :: c8:c9:c10:c11:c12 fib :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add sel :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add hole_c1_13 :: c hole_0':s:cons:n__fib1:n__add2_13 :: 0':s:cons:n__fib1:n__add hole_c6:c73_13 :: c6:c7 hole_c1:c24_13 :: c1:c2 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c8:c9:c10:c11:c126_13 :: c8:c9:c10:c11:c12 gen_0':s:cons:n__fib1:n__add7_13 :: Nat -> 0':s:cons:n__fib1:n__add gen_c6:c78_13 :: Nat -> c6:c7 gen_c3:c4:c59_13 :: Nat -> c3:c4:c5 gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: SEL, ADD, activate, ACTIVATE, sel, add They will be analysed ascendingly in the following order: activate < SEL ACTIVATE < SEL ADD < ACTIVATE activate < ACTIVATE activate < sel add < activate ---------------------------------------- (14) Obligation: Innermost TRS: Rules: FIB(z0) -> c(SEL(z0, fib1(s(0'), s(0'))), FIB1(s(0'), s(0'))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0', z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0', cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 fib(z0) -> sel(z0, fib1(s(0'), s(0'))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0', z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0', cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Types: FIB :: 0':s:cons:n__fib1:n__add -> c c :: c6:c7 -> c1:c2 -> c SEL :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c6:c7 fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add s :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add 0' :: 0':s:cons:n__fib1:n__add FIB1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c1:c2 c1 :: c1:c2 c2 :: c1:c2 ADD :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c3:c4:c5 c3 :: c3:c4:c5 c4 :: c3:c4:c5 -> c3:c4:c5 c5 :: c3:c4:c5 cons :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c6 :: c6:c7 c7 :: c6:c7 -> c8:c9:c10:c11:c12 -> c6:c7 activate :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add ACTIVATE :: 0':s:cons:n__fib1:n__add -> c8:c9:c10:c11:c12 n__fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c8 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c9 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 n__add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c10 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c11 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c12 :: c8:c9:c10:c11:c12 fib :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add sel :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add hole_c1_13 :: c hole_0':s:cons:n__fib1:n__add2_13 :: 0':s:cons:n__fib1:n__add hole_c6:c73_13 :: c6:c7 hole_c1:c24_13 :: c1:c2 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c8:c9:c10:c11:c126_13 :: c8:c9:c10:c11:c12 gen_0':s:cons:n__fib1:n__add7_13 :: Nat -> 0':s:cons:n__fib1:n__add gen_c6:c78_13 :: Nat -> c6:c7 gen_c3:c4:c59_13 :: Nat -> c3:c4:c5 gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12 Generator Equations: gen_0':s:cons:n__fib1:n__add7_13(0) <=> 0' gen_0':s:cons:n__fib1:n__add7_13(+(x, 1)) <=> s(gen_0':s:cons:n__fib1:n__add7_13(x)) gen_c6:c78_13(0) <=> c6 gen_c6:c78_13(+(x, 1)) <=> c7(gen_c6:c78_13(x), c12) gen_c3:c4:c59_13(0) <=> c3 gen_c3:c4:c59_13(+(x, 1)) <=> c4(gen_c3:c4:c59_13(x)) gen_c8:c9:c10:c11:c1210_13(0) <=> c12 gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c1, gen_c8:c9:c10:c11:c1210_13(x)) The following defined symbols remain to be analysed: ADD, SEL, activate, ACTIVATE, sel, add They will be analysed ascendingly in the following order: activate < SEL ACTIVATE < SEL ADD < ACTIVATE activate < ACTIVATE activate < sel add < activate ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: ADD(gen_0':s:cons:n__fib1:n__add7_13(n12_13), gen_0':s:cons:n__fib1:n__add7_13(b)) -> gen_c3:c4:c59_13(n12_13), rt in Omega(1 + n12_13) Induction Base: ADD(gen_0':s:cons:n__fib1:n__add7_13(0), gen_0':s:cons:n__fib1:n__add7_13(b)) ->_R^Omega(1) c3 Induction Step: ADD(gen_0':s:cons:n__fib1:n__add7_13(+(n12_13, 1)), gen_0':s:cons:n__fib1:n__add7_13(b)) ->_R^Omega(1) c4(ADD(gen_0':s:cons:n__fib1:n__add7_13(n12_13), gen_0':s:cons:n__fib1:n__add7_13(b))) ->_IH c4(gen_c3:c4:c59_13(c13_13)) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (16) Complex Obligation (BEST) ---------------------------------------- (17) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: FIB(z0) -> c(SEL(z0, fib1(s(0'), s(0'))), FIB1(s(0'), s(0'))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0', z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0', cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 fib(z0) -> sel(z0, fib1(s(0'), s(0'))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0', z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0', cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Types: FIB :: 0':s:cons:n__fib1:n__add -> c c :: c6:c7 -> c1:c2 -> c SEL :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c6:c7 fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add s :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add 0' :: 0':s:cons:n__fib1:n__add FIB1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c1:c2 c1 :: c1:c2 c2 :: c1:c2 ADD :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c3:c4:c5 c3 :: c3:c4:c5 c4 :: c3:c4:c5 -> c3:c4:c5 c5 :: c3:c4:c5 cons :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c6 :: c6:c7 c7 :: c6:c7 -> c8:c9:c10:c11:c12 -> c6:c7 activate :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add ACTIVATE :: 0':s:cons:n__fib1:n__add -> c8:c9:c10:c11:c12 n__fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c8 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c9 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 n__add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c10 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c11 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c12 :: c8:c9:c10:c11:c12 fib :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add sel :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add hole_c1_13 :: c hole_0':s:cons:n__fib1:n__add2_13 :: 0':s:cons:n__fib1:n__add hole_c6:c73_13 :: c6:c7 hole_c1:c24_13 :: c1:c2 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c8:c9:c10:c11:c126_13 :: c8:c9:c10:c11:c12 gen_0':s:cons:n__fib1:n__add7_13 :: Nat -> 0':s:cons:n__fib1:n__add gen_c6:c78_13 :: Nat -> c6:c7 gen_c3:c4:c59_13 :: Nat -> c3:c4:c5 gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12 Generator Equations: gen_0':s:cons:n__fib1:n__add7_13(0) <=> 0' gen_0':s:cons:n__fib1:n__add7_13(+(x, 1)) <=> s(gen_0':s:cons:n__fib1:n__add7_13(x)) gen_c6:c78_13(0) <=> c6 gen_c6:c78_13(+(x, 1)) <=> c7(gen_c6:c78_13(x), c12) gen_c3:c4:c59_13(0) <=> c3 gen_c3:c4:c59_13(+(x, 1)) <=> c4(gen_c3:c4:c59_13(x)) gen_c8:c9:c10:c11:c1210_13(0) <=> c12 gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c1, gen_c8:c9:c10:c11:c1210_13(x)) The following defined symbols remain to be analysed: ADD, SEL, activate, ACTIVATE, sel, add They will be analysed ascendingly in the following order: activate < SEL ACTIVATE < SEL ADD < ACTIVATE activate < ACTIVATE activate < sel add < activate ---------------------------------------- (18) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (19) BOUNDS(n^1, INF) ---------------------------------------- (20) Obligation: Innermost TRS: Rules: FIB(z0) -> c(SEL(z0, fib1(s(0'), s(0'))), FIB1(s(0'), s(0'))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0', z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0', cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 fib(z0) -> sel(z0, fib1(s(0'), s(0'))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0', z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0', cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Types: FIB :: 0':s:cons:n__fib1:n__add -> c c :: c6:c7 -> c1:c2 -> c SEL :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c6:c7 fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add s :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add 0' :: 0':s:cons:n__fib1:n__add FIB1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c1:c2 c1 :: c1:c2 c2 :: c1:c2 ADD :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c3:c4:c5 c3 :: c3:c4:c5 c4 :: c3:c4:c5 -> c3:c4:c5 c5 :: c3:c4:c5 cons :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c6 :: c6:c7 c7 :: c6:c7 -> c8:c9:c10:c11:c12 -> c6:c7 activate :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add ACTIVATE :: 0':s:cons:n__fib1:n__add -> c8:c9:c10:c11:c12 n__fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c8 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c9 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 n__add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c10 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c11 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c12 :: c8:c9:c10:c11:c12 fib :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add sel :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add hole_c1_13 :: c hole_0':s:cons:n__fib1:n__add2_13 :: 0':s:cons:n__fib1:n__add hole_c6:c73_13 :: c6:c7 hole_c1:c24_13 :: c1:c2 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c8:c9:c10:c11:c126_13 :: c8:c9:c10:c11:c12 gen_0':s:cons:n__fib1:n__add7_13 :: Nat -> 0':s:cons:n__fib1:n__add gen_c6:c78_13 :: Nat -> c6:c7 gen_c3:c4:c59_13 :: Nat -> c3:c4:c5 gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12 Lemmas: ADD(gen_0':s:cons:n__fib1:n__add7_13(n12_13), gen_0':s:cons:n__fib1:n__add7_13(b)) -> gen_c3:c4:c59_13(n12_13), rt in Omega(1 + n12_13) Generator Equations: gen_0':s:cons:n__fib1:n__add7_13(0) <=> 0' gen_0':s:cons:n__fib1:n__add7_13(+(x, 1)) <=> s(gen_0':s:cons:n__fib1:n__add7_13(x)) gen_c6:c78_13(0) <=> c6 gen_c6:c78_13(+(x, 1)) <=> c7(gen_c6:c78_13(x), c12) gen_c3:c4:c59_13(0) <=> c3 gen_c3:c4:c59_13(+(x, 1)) <=> c4(gen_c3:c4:c59_13(x)) gen_c8:c9:c10:c11:c1210_13(0) <=> c12 gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c1, gen_c8:c9:c10:c11:c1210_13(x)) The following defined symbols remain to be analysed: add, SEL, activate, ACTIVATE, sel They will be analysed ascendingly in the following order: activate < SEL ACTIVATE < SEL activate < ACTIVATE activate < sel add < activate ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: add(gen_0':s:cons:n__fib1:n__add7_13(n763_13), gen_0':s:cons:n__fib1:n__add7_13(b)) -> gen_0':s:cons:n__fib1:n__add7_13(+(n763_13, b)), rt in Omega(0) Induction Base: add(gen_0':s:cons:n__fib1:n__add7_13(0), gen_0':s:cons:n__fib1:n__add7_13(b)) ->_R^Omega(0) gen_0':s:cons:n__fib1:n__add7_13(b) Induction Step: add(gen_0':s:cons:n__fib1:n__add7_13(+(n763_13, 1)), gen_0':s:cons:n__fib1:n__add7_13(b)) ->_R^Omega(0) s(add(gen_0':s:cons:n__fib1:n__add7_13(n763_13), gen_0':s:cons:n__fib1:n__add7_13(b))) ->_IH s(gen_0':s:cons:n__fib1:n__add7_13(+(b, c764_13))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (22) Obligation: Innermost TRS: Rules: FIB(z0) -> c(SEL(z0, fib1(s(0'), s(0'))), FIB1(s(0'), s(0'))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0', z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0', cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 fib(z0) -> sel(z0, fib1(s(0'), s(0'))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0', z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0', cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Types: FIB :: 0':s:cons:n__fib1:n__add -> c c :: c6:c7 -> c1:c2 -> c SEL :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c6:c7 fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add s :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add 0' :: 0':s:cons:n__fib1:n__add FIB1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c1:c2 c1 :: c1:c2 c2 :: c1:c2 ADD :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> c3:c4:c5 c3 :: c3:c4:c5 c4 :: c3:c4:c5 -> c3:c4:c5 c5 :: c3:c4:c5 cons :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c6 :: c6:c7 c7 :: c6:c7 -> c8:c9:c10:c11:c12 -> c6:c7 activate :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add ACTIVATE :: 0':s:cons:n__fib1:n__add -> c8:c9:c10:c11:c12 n__fib1 :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c8 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c9 :: c1:c2 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 n__add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add c10 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c11 :: c3:c4:c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12 c12 :: c8:c9:c10:c11:c12 fib :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add sel :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add add :: 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add -> 0':s:cons:n__fib1:n__add hole_c1_13 :: c hole_0':s:cons:n__fib1:n__add2_13 :: 0':s:cons:n__fib1:n__add hole_c6:c73_13 :: c6:c7 hole_c1:c24_13 :: c1:c2 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c8:c9:c10:c11:c126_13 :: c8:c9:c10:c11:c12 gen_0':s:cons:n__fib1:n__add7_13 :: Nat -> 0':s:cons:n__fib1:n__add gen_c6:c78_13 :: Nat -> c6:c7 gen_c3:c4:c59_13 :: Nat -> c3:c4:c5 gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12 Lemmas: ADD(gen_0':s:cons:n__fib1:n__add7_13(n12_13), gen_0':s:cons:n__fib1:n__add7_13(b)) -> gen_c3:c4:c59_13(n12_13), rt in Omega(1 + n12_13) add(gen_0':s:cons:n__fib1:n__add7_13(n763_13), gen_0':s:cons:n__fib1:n__add7_13(b)) -> gen_0':s:cons:n__fib1:n__add7_13(+(n763_13, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:n__fib1:n__add7_13(0) <=> 0' gen_0':s:cons:n__fib1:n__add7_13(+(x, 1)) <=> s(gen_0':s:cons:n__fib1:n__add7_13(x)) gen_c6:c78_13(0) <=> c6 gen_c6:c78_13(+(x, 1)) <=> c7(gen_c6:c78_13(x), c12) gen_c3:c4:c59_13(0) <=> c3 gen_c3:c4:c59_13(+(x, 1)) <=> c4(gen_c3:c4:c59_13(x)) gen_c8:c9:c10:c11:c1210_13(0) <=> c12 gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c1, gen_c8:c9:c10:c11:c1210_13(x)) The following defined symbols remain to be analysed: activate, SEL, ACTIVATE, sel They will be analysed ascendingly in the following order: activate < SEL ACTIVATE < SEL activate < ACTIVATE activate < sel ---------------------------------------- (23) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (24) 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: fib(N) -> sel(N, fib1(s(0), s(0))) [1] fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) [1] add(0, X) -> X [1] add(s(X), Y) -> s(add(X, Y)) [1] sel(0, cons(X, XS)) -> X [1] sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1] fib1(X1, X2) -> n__fib1(X1, X2) [1] add(X1, X2) -> n__add(X1, X2) [1] activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) [1] activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) [1] activate(X) -> X [1] Rewrite Strategy: INNERMOST ---------------------------------------- (25) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: fib(N) -> sel(N, fib1(s(0), s(0))) [1] fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) [1] add(0, X) -> X [1] add(s(X), Y) -> s(add(X, Y)) [1] sel(0, cons(X, XS)) -> X [1] sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1] fib1(X1, X2) -> n__fib1(X1, X2) [1] add(X1, X2) -> n__add(X1, X2) [1] activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) [1] activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) [1] activate(X) -> X [1] The TRS has the following type information: fib :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons sel :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons fib1 :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons s :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons 0 :: 0:s:n__add:n__fib1:cons cons :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons n__fib1 :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons n__add :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons add :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons activate :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons Rewrite Strategy: INNERMOST ---------------------------------------- (27) 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: fib_1 sel_2 (c) The following functions are completely defined: activate_1 fib1_2 add_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (28) 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: fib(N) -> sel(N, fib1(s(0), s(0))) [1] fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) [1] add(0, X) -> X [1] add(s(X), Y) -> s(add(X, Y)) [1] sel(0, cons(X, XS)) -> X [1] sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1] fib1(X1, X2) -> n__fib1(X1, X2) [1] add(X1, X2) -> n__add(X1, X2) [1] activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) [1] activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) [1] activate(X) -> X [1] The TRS has the following type information: fib :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons sel :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons fib1 :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons s :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons 0 :: 0:s:n__add:n__fib1:cons cons :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons n__fib1 :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons n__add :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons add :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons activate :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons Rewrite Strategy: INNERMOST ---------------------------------------- (29) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (30) 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: fib(N) -> sel(N, cons(s(0), n__fib1(s(0), n__add(s(0), s(0))))) [2] fib(N) -> sel(N, n__fib1(s(0), s(0))) [2] fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) [1] add(0, X) -> X [1] add(s(X), Y) -> s(add(X, Y)) [1] sel(0, cons(X, XS)) -> X [1] sel(s(N), cons(X, n__fib1(X1', X2'))) -> sel(N, fib1(activate(X1'), activate(X2'))) [2] sel(s(N), cons(X, n__add(X1'', X2''))) -> sel(N, add(activate(X1''), activate(X2''))) [2] sel(s(N), cons(X, XS)) -> sel(N, XS) [2] fib1(X1, X2) -> n__fib1(X1, X2) [1] add(X1, X2) -> n__add(X1, X2) [1] activate(n__fib1(n__fib1(X11, X21), n__fib1(X13, X23))) -> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) [3] activate(n__fib1(n__fib1(X11, X21), n__add(X14, X24))) -> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) [3] activate(n__fib1(n__fib1(X11, X21), X2)) -> fib1(fib1(activate(X11), activate(X21)), X2) [3] activate(n__fib1(n__add(X12, X22), n__fib1(X15, X25))) -> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) [3] activate(n__fib1(n__add(X12, X22), n__add(X16, X26))) -> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) [3] activate(n__fib1(n__add(X12, X22), X2)) -> fib1(add(activate(X12), activate(X22)), X2) [3] activate(n__fib1(X1, n__fib1(X17, X27))) -> fib1(X1, fib1(activate(X17), activate(X27))) [3] activate(n__fib1(X1, n__add(X18, X28))) -> fib1(X1, add(activate(X18), activate(X28))) [3] activate(n__fib1(X1, X2)) -> fib1(X1, X2) [3] activate(n__add(n__fib1(X19, X29), n__fib1(X111, X211))) -> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) [3] activate(n__add(n__fib1(X19, X29), n__add(X112, X212))) -> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) [3] activate(n__add(n__fib1(X19, X29), X2)) -> add(fib1(activate(X19), activate(X29)), X2) [3] activate(n__add(n__add(X110, X210), n__fib1(X113, X213))) -> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) [3] activate(n__add(n__add(X110, X210), n__add(X114, X214))) -> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) [3] activate(n__add(n__add(X110, X210), X2)) -> add(add(activate(X110), activate(X210)), X2) [3] activate(n__add(X1, n__fib1(X115, X215))) -> add(X1, fib1(activate(X115), activate(X215))) [3] activate(n__add(X1, n__add(X116, X216))) -> add(X1, add(activate(X116), activate(X216))) [3] activate(n__add(X1, X2)) -> add(X1, X2) [3] activate(X) -> X [1] The TRS has the following type information: fib :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons sel :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons fib1 :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons s :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons 0 :: 0:s:n__add:n__fib1:cons cons :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons n__fib1 :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons n__add :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons add :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons activate :: 0:s:n__add:n__fib1:cons -> 0:s:n__add:n__fib1:cons Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 3 }-> fib1(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 add(z, z') -{ 1 }-> X :|: z' = X, X >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(X, Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 fib(z) -{ 2 }-> sel(N, 1 + (1 + 0) + (1 + 0)) :|: z = N, N >= 0 fib(z) -{ 2 }-> sel(N, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z = N, N >= 0 fib1(z, z') -{ 1 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: z' = Y, Y >= 0, X >= 0, z = X fib1(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(N, XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0 sel(z, z') -{ 2 }-> sel(N, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + N, X >= 0, z' = 1 + X + (1 + X1' + X2'), N >= 0 sel(z, z') -{ 2 }-> sel(N, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, z = 1 + N, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), N >= 0 ---------------------------------------- (33) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: fib1(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 fib1(z, z') -{ 1 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: z' = Y, Y >= 0, X >= 0, z = X ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> X :|: z' = X, X >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(X, Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 fib(z) -{ 2 }-> sel(N, 1 + (1 + 0) + (1 + 0)) :|: z = N, N >= 0 fib(z) -{ 2 }-> sel(N, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z = N, N >= 0 fib1(z, z') -{ 1 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: z' = Y, Y >= 0, X >= 0, z = X fib1(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(N, XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0 sel(z, z') -{ 2 }-> sel(N, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + N, X >= 0, z' = 1 + X + (1 + X1' + X2'), N >= 0 sel(z, z') -{ 2 }-> sel(N, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, z = 1 + N, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), N >= 0 ---------------------------------------- (35) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 ---------------------------------------- (37) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { add } { fib1 } { activate } { sel } { fib } ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {add}, {fib1}, {activate}, {sel}, {fib} ---------------------------------------- (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) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {add}, {fib1}, {activate}, {sel}, {fib} ---------------------------------------- (41) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: add after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z + z' ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {add}, {fib1}, {activate}, {sel}, {fib} Previous analysis results are: add: runtime: ?, size: O(n^1) [1 + z + z'] ---------------------------------------- (43) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: add after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {fib1}, {activate}, {sel}, {fib} Previous analysis results are: add: runtime: O(n^1) [1 + z], size: O(n^1) [1 + z + 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 + X1 }-> s' :|: s' >= 0, s' <= X1 + X2 + 1, X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 + z }-> 1 + s :|: s >= 0, s <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {fib1}, {activate}, {sel}, {fib} Previous analysis results are: add: runtime: O(n^1) [1 + z], size: O(n^1) [1 + z + z'] ---------------------------------------- (47) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: fib1 after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 3 + 2*z + 2*z' ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 + X1 }-> s' :|: s' >= 0, s' <= X1 + X2 + 1, X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 + z }-> 1 + s :|: s >= 0, s <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {fib1}, {activate}, {sel}, {fib} Previous analysis results are: add: runtime: O(n^1) [1 + z], size: O(n^1) [1 + z + z'] fib1: runtime: ?, size: O(n^1) [3 + 2*z + 2*z'] ---------------------------------------- (49) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: fib1 after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 + X1 }-> s' :|: s' >= 0, s' <= X1 + X2 + 1, X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 + z }-> 1 + s :|: s >= 0, s <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {activate}, {sel}, {fib} Previous analysis results are: add: runtime: O(n^1) [1 + z], size: O(n^1) [1 + z + z'] fib1: runtime: O(1) [1], size: O(n^1) [3 + 2*z + 2*z'] ---------------------------------------- (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 + X1 }-> s' :|: s' >= 0, s' <= X1 + X2 + 1, X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 3 }-> fib1(X1, fib1(activate(X17), activate(X27))) :|: X1 >= 0, X17 >= 0, X27 >= 0, z = 1 + X1 + (1 + X17 + X27) activate(z) -{ 3 }-> fib1(X1, add(activate(X18), activate(X28))) :|: X1 >= 0, X18 >= 0, X28 >= 0, z = 1 + X1 + (1 + X18 + X28) activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), fib1(activate(X13), activate(X23))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X13 + X23), X13 >= 0, X23 >= 0 activate(z) -{ 3 }-> fib1(fib1(activate(X11), activate(X21)), add(activate(X14), activate(X24))) :|: X11 >= 0, X21 >= 0, z = 1 + (1 + X11 + X21) + (1 + X14 + X24), X14 >= 0, X24 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), fib1(activate(X15), activate(X25))) :|: z = 1 + (1 + X12 + X22) + (1 + X15 + X25), X12 >= 0, X22 >= 0, X15 >= 0, X25 >= 0 activate(z) -{ 3 }-> fib1(add(activate(X12), activate(X22)), add(activate(X16), activate(X26))) :|: X12 >= 0, X22 >= 0, X16 >= 0, X26 >= 0, z = 1 + (1 + X12 + X22) + (1 + X16 + X26) activate(z) -{ 3 }-> add(X1, fib1(activate(X115), activate(X215))) :|: X1 >= 0, z = 1 + X1 + (1 + X115 + X215), X115 >= 0, X215 >= 0 activate(z) -{ 3 }-> add(X1, add(activate(X116), activate(X216))) :|: X1 >= 0, X216 >= 0, X116 >= 0, z = 1 + X1 + (1 + X116 + X216) activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), X2) :|: z = 1 + (1 + X19 + X29) + X2, X29 >= 0, X19 >= 0, X2 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), fib1(activate(X111), activate(X211))) :|: X29 >= 0, X19 >= 0, X211 >= 0, z = 1 + (1 + X19 + X29) + (1 + X111 + X211), X111 >= 0 activate(z) -{ 3 }-> add(fib1(activate(X19), activate(X29)), add(activate(X112), activate(X212))) :|: X212 >= 0, X29 >= 0, X19 >= 0, X112 >= 0, z = 1 + (1 + X19 + X29) + (1 + X112 + X212) activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), X2) :|: z = 1 + (1 + X110 + X210) + X2, X110 >= 0, X2 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), fib1(activate(X113), activate(X213))) :|: X110 >= 0, z = 1 + (1 + X110 + X210) + (1 + X113 + X213), X113 >= 0, X213 >= 0, X210 >= 0 activate(z) -{ 3 }-> add(add(activate(X110), activate(X210)), add(activate(X114), activate(X214))) :|: X110 >= 0, X114 >= 0, X214 >= 0, z = 1 + (1 + X110 + X210) + (1 + X114 + X214), X210 >= 0 activate(z) -{ 4 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X2 = Y, Y >= 0, X >= 0, X1 = X activate(z) -{ 4 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' add(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 1 + z }-> 1 + s :|: s >= 0, s <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 fib(z) -{ 2 }-> sel(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 fib1(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 fib1(z, z') -{ 1 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, fib1(activate(X1'), activate(X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0 sel(z, z') -{ 2 }-> sel(z - 1, add(activate(X1''), activate(X2''))) :|: X1'' >= 0, X >= 0, X2'' >= 0, z' = 1 + X + (1 + X1'' + X2''), z - 1 >= 0 Function symbols to be analyzed: {activate}, {sel}, {fib} Previous analysis results are: add: runtime: O(n^1) [1 + z], size: O(n^1) [1 + z + z'] fib1: runtime: O(1) [1], size: O(n^1) [3 + 2*z + 2*z'] ---------------------------------------- (53) 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: sel(v0, v1) -> null_sel [0] And the following fresh constants: null_sel ---------------------------------------- (54) 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: fib(N) -> sel(N, fib1(s(0), s(0))) [1] fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) [1] add(0, X) -> X [1] add(s(X), Y) -> s(add(X, Y)) [1] sel(0, cons(X, XS)) -> X [1] sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1] fib1(X1, X2) -> n__fib1(X1, X2) [1] add(X1, X2) -> n__add(X1, X2) [1] activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) [1] activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) [1] activate(X) -> X [1] sel(v0, v1) -> null_sel [0] The TRS has the following type information: fib :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel sel :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel fib1 :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel s :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel 0 :: 0:s:n__add:n__fib1:cons:null_sel cons :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel n__fib1 :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel n__add :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel add :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel activate :: 0:s:n__add:n__fib1:cons:null_sel -> 0:s:n__add:n__fib1:cons:null_sel null_sel :: 0:s:n__add:n__fib1:cons:null_sel Rewrite Strategy: INNERMOST ---------------------------------------- (55) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 null_sel => 0 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> fib1(activate(X1), activate(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 1 }-> add(activate(X1), activate(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 add(z, z') -{ 1 }-> X :|: z' = X, X >= 0, z = 0 add(z, z') -{ 1 }-> 1 + add(X, Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 fib(z) -{ 1 }-> sel(N, fib1(1 + 0, 1 + 0)) :|: z = N, N >= 0 fib1(z, z') -{ 1 }-> 1 + X + (1 + Y + (1 + X + Y)) :|: z' = Y, Y >= 0, X >= 0, z = X fib1(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0 sel(z, z') -{ 1 }-> sel(N, activate(XS)) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0 sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (57) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: fib(z0) -> sel(z0, fib1(s(0), s(0))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0, z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0, cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 S tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) FIB1(z0, z1) -> c1 FIB1(z0, z1) -> c2 ADD(0, z0) -> c3 ADD(s(z0), z1) -> c4(ADD(z0, z1)) ADD(z0, z1) -> c5 SEL(0, cons(z0, z1)) -> c6 SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(z0) -> c12 K tuples:none Defined Rule Symbols: fib_1, fib1_2, add_2, sel_2, activate_1 Defined Pair Symbols: FIB_1, FIB1_2, ADD_2, SEL_2, ACTIVATE_1 Compound Symbols: c_2, c1, c2, c3, c4_1, c5, c6, c7_2, c8_2, c9_2, c10_2, c11_2, c12 ---------------------------------------- (59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: SEL(0, cons(z0, z1)) -> c6 FIB1(z0, z1) -> c1 ADD(z0, z1) -> c5 FIB1(z0, z1) -> c2 ACTIVATE(z0) -> c12 ADD(0, z0) -> c3 ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: fib(z0) -> sel(z0, fib1(s(0), s(0))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) S tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0))) ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__fib1(z0, z1)) -> c8(FIB1(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(FIB1(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) K tuples:none Defined Rule Symbols: fib_1, fib1_2, add_2, sel_2, activate_1 Defined Pair Symbols: FIB_1, ADD_2, SEL_2, ACTIVATE_1 Compound Symbols: c_2, c4_1, c7_2, c8_2, c9_2, c10_2, c11_2 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: fib(z0) -> sel(z0, fib1(s(0), s(0))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) K tuples:none Defined Rule Symbols: fib_1, fib1_2, add_2, sel_2, activate_1 Defined Pair Symbols: ADD_2, SEL_2, ACTIVATE_1, FIB_1 Compound Symbols: c4_1, c7_2, c10_2, c11_2, c_1, c8_1, c9_1 ---------------------------------------- (63) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: fib(z0) -> sel(z0, fib1(s(0), s(0))) fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) Defined Rule Symbols: fib_1, fib1_2, add_2, sel_2, activate_1 Defined Pair Symbols: ADD_2, SEL_2, ACTIVATE_1, FIB_1 Compound Symbols: c4_1, c7_2, c10_2, c11_2, c_1, c8_1, c9_1 ---------------------------------------- (65) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: fib(z0) -> sel(z0, fib1(s(0), s(0))) sel(0, cons(z0, z1)) -> z0 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, SEL_2, ACTIVATE_1, FIB_1 Compound Symbols: c4_1, c7_2, c10_2, c11_2, c_1, c8_1, c9_1 ---------------------------------------- (67) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (68) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) The (relative) TRS S consists of the following rules: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Rewrite Strategy: INNERMOST ---------------------------------------- (69) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (70) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (71) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (72) 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: ADD(s(z0), z1) -> c4(ADD(z0, z1)) [1] SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) [1] ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) [1] ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) [1] FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) [0] activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) [0] activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) [0] activate(z0) -> z0 [0] fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) [0] fib1(z0, z1) -> n__fib1(z0, z1) [0] add(0, z0) -> z0 [0] add(s(z0), z1) -> s(add(z0, z1)) [0] add(z0, z1) -> n__add(z0, z1) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (73) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (74) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: ADD(s(z0), z1) -> c4(ADD(z0, z1)) [1] SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) [1] ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) [1] ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) [1] FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) [0] activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) [0] activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) [0] activate(z0) -> z0 [0] fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) [0] fib1(z0, z1) -> n__fib1(z0, z1) [0] add(0, z0) -> z0 [0] add(s(z0), z1) -> s(add(z0, z1)) [0] add(z0, z1) -> n__add(z0, z1) [0] The TRS has the following type information: ADD :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> c4 s :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c4 :: c4 -> c4 SEL :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> c7 cons :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c7 :: c7 -> c10:c11:c8:c9 -> c7 activate :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 ACTIVATE :: s:cons:n__add:n__fib1:0 -> c10:c11:c8:c9 n__add :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c10 :: c4 -> c10:c11:c8:c9 -> c10:c11:c8:c9 c11 :: c4 -> c10:c11:c8:c9 -> c10:c11:c8:c9 n__fib1 :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c8 :: c10:c11:c8:c9 -> c10:c11:c8:c9 c9 :: c10:c11:c8:c9 -> c10:c11:c8:c9 FIB :: s:cons:n__add:n__fib1:0 -> c c :: c7 -> c fib1 :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 0 :: s:cons:n__add:n__fib1:0 add :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 Rewrite Strategy: INNERMOST ---------------------------------------- (75) 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: ADD_2 SEL_2 ACTIVATE_1 (c) The following functions are completely defined: FIB_1 activate_1 fib1_2 add_2 Due to the following rules being added: FIB(v0) -> const3 [0] activate(v0) -> 0 [0] fib1(v0, v1) -> 0 [0] add(v0, v1) -> 0 [0] And the following fresh constants: const3, const, const1, const2 ---------------------------------------- (76) 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: ADD(s(z0), z1) -> c4(ADD(z0, z1)) [1] SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) [1] ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) [1] ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) [1] FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) [0] activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) [0] activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) [0] activate(z0) -> z0 [0] fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) [0] fib1(z0, z1) -> n__fib1(z0, z1) [0] add(0, z0) -> z0 [0] add(s(z0), z1) -> s(add(z0, z1)) [0] add(z0, z1) -> n__add(z0, z1) [0] FIB(v0) -> const3 [0] activate(v0) -> 0 [0] fib1(v0, v1) -> 0 [0] add(v0, v1) -> 0 [0] The TRS has the following type information: ADD :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> c4 s :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c4 :: c4 -> c4 SEL :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> c7 cons :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c7 :: c7 -> c10:c11:c8:c9 -> c7 activate :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 ACTIVATE :: s:cons:n__add:n__fib1:0 -> c10:c11:c8:c9 n__add :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c10 :: c4 -> c10:c11:c8:c9 -> c10:c11:c8:c9 c11 :: c4 -> c10:c11:c8:c9 -> c10:c11:c8:c9 n__fib1 :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c8 :: c10:c11:c8:c9 -> c10:c11:c8:c9 c9 :: c10:c11:c8:c9 -> c10:c11:c8:c9 FIB :: s:cons:n__add:n__fib1:0 -> c:const3 c :: c7 -> c:const3 fib1 :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 0 :: s:cons:n__add:n__fib1:0 add :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 const3 :: c:const3 const :: c4 const1 :: c7 const2 :: c10:c11:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (77) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (78) 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: ADD(s(z0), z1) -> c4(ADD(z0, z1)) [1] SEL(s(z0), cons(z1, n__fib1(z0', z1'))) -> c7(SEL(z0, fib1(activate(z0'), activate(z1'))), ACTIVATE(n__fib1(z0', z1'))) [1] SEL(s(z0), cons(z1, n__add(z0'', z1''))) -> c7(SEL(z0, add(activate(z0''), activate(z1''))), ACTIVATE(n__add(z0'', z1''))) [1] SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, z2), ACTIVATE(z2)) [1] SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, 0), ACTIVATE(z2)) [1] ACTIVATE(n__add(n__fib1(z01, z11), n__fib1(z03, z13))) -> c10(ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))), ACTIVATE(n__fib1(z01, z11))) [1] ACTIVATE(n__add(n__fib1(z01, z11), n__add(z04, z14))) -> c10(ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))), ACTIVATE(n__fib1(z01, z11))) [1] ACTIVATE(n__add(n__fib1(z01, z11), z1)) -> c10(ADD(fib1(activate(z01), activate(z11)), z1), ACTIVATE(n__fib1(z01, z11))) [1] ACTIVATE(n__add(n__fib1(z01, z11), z1)) -> c10(ADD(fib1(activate(z01), activate(z11)), 0), ACTIVATE(n__fib1(z01, z11))) [1] ACTIVATE(n__add(n__add(z02, z12), n__fib1(z05, z15))) -> c10(ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))), ACTIVATE(n__add(z02, z12))) [1] ACTIVATE(n__add(n__add(z02, z12), n__add(z06, z16))) -> c10(ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))), ACTIVATE(n__add(z02, z12))) [1] ACTIVATE(n__add(n__add(z02, z12), z1)) -> c10(ADD(add(activate(z02), activate(z12)), z1), ACTIVATE(n__add(z02, z12))) [1] ACTIVATE(n__add(n__add(z02, z12), z1)) -> c10(ADD(add(activate(z02), activate(z12)), 0), ACTIVATE(n__add(z02, z12))) [1] ACTIVATE(n__add(z0, n__fib1(z07, z17))) -> c10(ADD(z0, fib1(activate(z07), activate(z17))), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, n__add(z08, z18))) -> c10(ADD(z0, add(activate(z08), activate(z18))), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(z0, z1), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(z0, 0), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, n__fib1(z09, z19))) -> c10(ADD(0, fib1(activate(z09), activate(z19))), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, n__add(z010, z110))) -> c10(ADD(0, add(activate(z010), activate(z110))), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(0, z1), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(0, 0), ACTIVATE(z0)) [1] ACTIVATE(n__add(n__fib1(z011, z111), n__fib1(z013, z113))) -> c11(ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))), ACTIVATE(n__fib1(z013, z113))) [1] ACTIVATE(n__add(n__fib1(z011, z111), n__add(z014, z114))) -> c11(ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))), ACTIVATE(n__add(z014, z114))) [1] ACTIVATE(n__add(n__fib1(z011, z111), z1)) -> c11(ADD(fib1(activate(z011), activate(z111)), z1), ACTIVATE(z1)) [1] ACTIVATE(n__add(n__fib1(z011, z111), z1)) -> c11(ADD(fib1(activate(z011), activate(z111)), 0), ACTIVATE(z1)) [1] ACTIVATE(n__add(n__add(z012, z112), n__fib1(z015, z115))) -> c11(ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))), ACTIVATE(n__fib1(z015, z115))) [1] ACTIVATE(n__add(n__add(z012, z112), n__add(z016, z116))) -> c11(ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))), ACTIVATE(n__add(z016, z116))) [1] ACTIVATE(n__add(n__add(z012, z112), z1)) -> c11(ADD(add(activate(z012), activate(z112)), z1), ACTIVATE(z1)) [1] ACTIVATE(n__add(n__add(z012, z112), z1)) -> c11(ADD(add(activate(z012), activate(z112)), 0), ACTIVATE(z1)) [1] ACTIVATE(n__add(z0, n__fib1(z017, z117))) -> c11(ADD(z0, fib1(activate(z017), activate(z117))), ACTIVATE(n__fib1(z017, z117))) [1] ACTIVATE(n__add(z0, n__add(z018, z118))) -> c11(ADD(z0, add(activate(z018), activate(z118))), ACTIVATE(n__add(z018, z118))) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(z0, z1), ACTIVATE(z1)) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(z0, 0), ACTIVATE(z1)) [1] ACTIVATE(n__add(z0, n__fib1(z019, z119))) -> c11(ADD(0, fib1(activate(z019), activate(z119))), ACTIVATE(n__fib1(z019, z119))) [1] ACTIVATE(n__add(z0, n__add(z020, z120))) -> c11(ADD(0, add(activate(z020), activate(z120))), ACTIVATE(n__add(z020, z120))) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(0, z1), ACTIVATE(z1)) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(0, 0), ACTIVATE(z1)) [1] ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) [1] ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) [1] FIB(z0) -> c(SEL(z0, cons(s(0), n__fib1(s(0), n__add(s(0), s(0)))))) [0] FIB(z0) -> c(SEL(z0, n__fib1(s(0), s(0)))) [0] FIB(z0) -> c(SEL(z0, 0)) [0] activate(n__fib1(n__fib1(z021, z121), n__fib1(z023, z123))) -> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) [0] activate(n__fib1(n__fib1(z021, z121), n__add(z024, z124))) -> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) [0] activate(n__fib1(n__fib1(z021, z121), z1)) -> fib1(fib1(activate(z021), activate(z121)), z1) [0] activate(n__fib1(n__fib1(z021, z121), z1)) -> fib1(fib1(activate(z021), activate(z121)), 0) [0] activate(n__fib1(n__add(z022, z122), n__fib1(z025, z125))) -> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) [0] activate(n__fib1(n__add(z022, z122), n__add(z026, z126))) -> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) [0] activate(n__fib1(n__add(z022, z122), z1)) -> fib1(add(activate(z022), activate(z122)), z1) [0] activate(n__fib1(n__add(z022, z122), z1)) -> fib1(add(activate(z022), activate(z122)), 0) [0] activate(n__fib1(z0, n__fib1(z027, z127))) -> fib1(z0, fib1(activate(z027), activate(z127))) [0] activate(n__fib1(z0, n__add(z028, z128))) -> fib1(z0, add(activate(z028), activate(z128))) [0] activate(n__fib1(z0, z1)) -> fib1(z0, z1) [0] activate(n__fib1(z0, z1)) -> fib1(z0, 0) [0] activate(n__fib1(z0, n__fib1(z029, z129))) -> fib1(0, fib1(activate(z029), activate(z129))) [0] activate(n__fib1(z0, n__add(z030, z130))) -> fib1(0, add(activate(z030), activate(z130))) [0] activate(n__fib1(z0, z1)) -> fib1(0, z1) [0] activate(n__fib1(z0, z1)) -> fib1(0, 0) [0] activate(n__add(n__fib1(z031, z131), n__fib1(z033, z133))) -> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) [0] activate(n__add(n__fib1(z031, z131), n__add(z034, z134))) -> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) [0] activate(n__add(n__fib1(z031, z131), z1)) -> add(fib1(activate(z031), activate(z131)), z1) [0] activate(n__add(n__fib1(z031, z131), z1)) -> add(fib1(activate(z031), activate(z131)), 0) [0] activate(n__add(n__add(z032, z132), n__fib1(z035, z135))) -> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) [0] activate(n__add(n__add(z032, z132), n__add(z036, z136))) -> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) [0] activate(n__add(n__add(z032, z132), z1)) -> add(add(activate(z032), activate(z132)), z1) [0] activate(n__add(n__add(z032, z132), z1)) -> add(add(activate(z032), activate(z132)), 0) [0] activate(n__add(z0, n__fib1(z037, z137))) -> add(z0, fib1(activate(z037), activate(z137))) [0] activate(n__add(z0, n__add(z038, z138))) -> add(z0, add(activate(z038), activate(z138))) [0] activate(n__add(z0, z1)) -> add(z0, z1) [0] activate(n__add(z0, z1)) -> add(z0, 0) [0] activate(n__add(z0, n__fib1(z039, z139))) -> add(0, fib1(activate(z039), activate(z139))) [0] activate(n__add(z0, n__add(z040, z140))) -> add(0, add(activate(z040), activate(z140))) [0] activate(n__add(z0, z1)) -> add(0, z1) [0] activate(n__add(z0, z1)) -> add(0, 0) [0] activate(z0) -> z0 [0] fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) [0] fib1(z0, z1) -> n__fib1(z0, z1) [0] add(0, z0) -> z0 [0] add(s(z0), z1) -> s(add(z0, z1)) [0] add(z0, z1) -> n__add(z0, z1) [0] FIB(v0) -> const3 [0] activate(v0) -> 0 [0] fib1(v0, v1) -> 0 [0] add(v0, v1) -> 0 [0] The TRS has the following type information: ADD :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> c4 s :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c4 :: c4 -> c4 SEL :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> c7 cons :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c7 :: c7 -> c10:c11:c8:c9 -> c7 activate :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 ACTIVATE :: s:cons:n__add:n__fib1:0 -> c10:c11:c8:c9 n__add :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c10 :: c4 -> c10:c11:c8:c9 -> c10:c11:c8:c9 c11 :: c4 -> c10:c11:c8:c9 -> c10:c11:c8:c9 n__fib1 :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 c8 :: c10:c11:c8:c9 -> c10:c11:c8:c9 c9 :: c10:c11:c8:c9 -> c10:c11:c8:c9 FIB :: s:cons:n__add:n__fib1:0 -> c:const3 c :: c7 -> c:const3 fib1 :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 0 :: s:cons:n__add:n__fib1:0 add :: s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 -> s:cons:n__add:n__fib1:0 const3 :: c:const3 const :: c4 const1 :: c7 const2 :: c10:c11:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (79) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 const3 => 0 const => 0 const1 => 0 const2 => 0 ---------------------------------------- (80) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 FIB(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 FIB(z) -{ 0 }-> 1 + SEL(z0, 0) :|: z = z0, z0 >= 0 FIB(z) -{ 0 }-> 1 + SEL(z0, 1 + (1 + 0) + (1 + 0)) :|: z = z0, z0 >= 0 FIB(z) -{ 0 }-> 1 + SEL(z0, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z = z0, z0 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z = 1 + z0, z1' >= 0, z0 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z = 1 + z0, z0 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> fib1(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> fib1(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 add(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 add(z, z') -{ 0 }-> 1 + add(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib1(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 1 + z0 + (1 + z1 + (1 + z0 + z1)) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 ---------------------------------------- (81) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: fib1(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 1 + z0 + (1 + z1 + (1 + z0 + z1)) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 ---------------------------------------- (82) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 FIB(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 FIB(z) -{ 0 }-> 1 + SEL(z0, 0) :|: z = z0, z0 >= 0 FIB(z) -{ 0 }-> 1 + SEL(z0, 1 + (1 + 0) + (1 + 0)) :|: z = z0, z0 >= 0 FIB(z) -{ 0 }-> 1 + SEL(z0, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z = z0, z0 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z = 1 + z0, z1' >= 0, z0 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z = 1 + z0, z0 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z0, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 add(z, z') -{ 0 }-> 1 + add(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib1(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 1 + z0 + (1 + z1 + (1 + z0 + z1)) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 ---------------------------------------- (83) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (84) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 ---------------------------------------- (85) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { ADD } { add } { fib1 } { activate } { ACTIVATE } { SEL } { FIB } ---------------------------------------- (86) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {ADD}, {add}, {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} ---------------------------------------- (87) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (88) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {ADD}, {add}, {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} ---------------------------------------- (89) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: ADD after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (90) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {ADD}, {add}, {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: ?, size: O(1) [0] ---------------------------------------- (91) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: ADD after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (92) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, 0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {add}, {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (93) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (94) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {add}, {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (95) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: add after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z + z' ---------------------------------------- (96) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {add}, {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] add: runtime: ?, size: O(n^1) [1 + z + z'] ---------------------------------------- (97) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: add after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (98) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> add(0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] add: runtime: O(1) [0], size: O(n^1) [1 + z + z'] ---------------------------------------- (99) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (100) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> s10 :|: s10 >= 0, s10 <= 0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s7 :|: s7 >= 0, s7 <= z0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s8 :|: s8 >= 0, s8 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s9 :|: s9 >= 0, s9 <= 0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] add: runtime: O(1) [0], size: O(n^1) [1 + z + z'] ---------------------------------------- (101) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: fib1 after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 3 + 2*z + 2*z' ---------------------------------------- (102) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> s10 :|: s10 >= 0, s10 <= 0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s7 :|: s7 >= 0, s7 <= z0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s8 :|: s8 >= 0, s8 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s9 :|: s9 >= 0, s9 <= 0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {fib1}, {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] add: runtime: O(1) [0], size: O(n^1) [1 + z + z'] fib1: runtime: ?, size: O(n^1) [3 + 2*z + 2*z'] ---------------------------------------- (103) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: fib1 after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (104) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> s10 :|: s10 >= 0, s10 <= 0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s7 :|: s7 >= 0, s7 <= z0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s8 :|: s8 >= 0, s8 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s9 :|: s9 >= 0, s9 <= 0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] add: runtime: O(1) [0], size: O(n^1) [1 + z + z'] fib1: runtime: O(1) [0], size: O(n^1) [3 + 2*z + 2*z'] ---------------------------------------- (105) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (106) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s' + ACTIVATE(z0) :|: s' >= 0, s' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s'' + ACTIVATE(z0) :|: s'' >= 0, s'' <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s1 + ACTIVATE(z0) :|: s1 >= 0, s1 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s2 + ACTIVATE(z0) :|: s2 >= 0, s2 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s3 + ACTIVATE(z1) :|: s3 >= 0, s3 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 + z0 }-> 1 + s4 + ACTIVATE(z1) :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s5 + ACTIVATE(z1) :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + s6 + ACTIVATE(z1) :|: s6 >= 0, s6 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z017), activate(z117))) + ACTIVATE(1 + z017 + z117) :|: z117 >= 0, z0 >= 0, z = 1 + z0 + (1 + z017 + z117), z017 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, fib1(activate(z07), activate(z17))) + ACTIVATE(z0) :|: z = 1 + z0 + (1 + z07 + z17), z07 >= 0, z17 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z018), activate(z118))) + ACTIVATE(1 + z018 + z118) :|: z118 >= 0, z = 1 + z0 + (1 + z018 + z118), z0 >= 0, z018 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(z0, add(activate(z08), activate(z18))) + ACTIVATE(z0) :|: z08 >= 0, z18 >= 0, z0 >= 0, z = 1 + z0 + (1 + z08 + z18) ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), z1) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), fib1(activate(z03), activate(z13))) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z = 1 + (1 + z01 + z11) + (1 + z03 + z13), z01 >= 0, z03 >= 0, z13 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), add(activate(z04), activate(z14))) + ACTIVATE(1 + z01 + z11) :|: z04 >= 0, z11 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + (1 + z04 + z14), z14 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z01), activate(z11)), 0) + ACTIVATE(1 + z01 + z11) :|: z11 >= 0, z1 >= 0, z01 >= 0, z = 1 + (1 + z01 + z11) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), z1) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), fib1(activate(z013), activate(z113))) + ACTIVATE(1 + z013 + z113) :|: z011 >= 0, z013 >= 0, z113 >= 0, z = 1 + (1 + z011 + z111) + (1 + z013 + z113), z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), add(activate(z014), activate(z114))) + ACTIVATE(1 + z014 + z114) :|: z011 >= 0, z114 >= 0, z = 1 + (1 + z011 + z111) + (1 + z014 + z114), z014 >= 0, z111 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(fib1(activate(z011), activate(z111)), 0) + ACTIVATE(z1) :|: z011 >= 0, z1 >= 0, z111 >= 0, z = 1 + (1 + z011 + z111) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), z1) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), fib1(activate(z015), activate(z115))) + ACTIVATE(1 + z015 + z115) :|: z015 >= 0, z112 >= 0, z115 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + (1 + z015 + z115) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), add(activate(z016), activate(z116))) + ACTIVATE(1 + z016 + z116) :|: z = 1 + (1 + z012 + z112) + (1 + z016 + z116), z112 >= 0, z012 >= 0, z016 >= 0, z116 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z012), activate(z112)), 0) + ACTIVATE(z1) :|: z1 >= 0, z112 >= 0, z012 >= 0, z = 1 + (1 + z012 + z112) + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), z1) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), fib1(activate(z05), activate(z15))) + ACTIVATE(1 + z02 + z12) :|: z15 >= 0, z02 >= 0, z12 >= 0, z05 >= 0, z = 1 + (1 + z02 + z12) + (1 + z05 + z15) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), add(activate(z06), activate(z16))) + ACTIVATE(1 + z02 + z12) :|: z02 >= 0, z06 >= 0, z12 >= 0, z16 >= 0, z = 1 + (1 + z02 + z12) + (1 + z06 + z16) ACTIVATE(z) -{ 1 }-> 1 + ADD(add(activate(z02), activate(z12)), 0) + ACTIVATE(1 + z02 + z12) :|: z1 >= 0, z = 1 + (1 + z02 + z12) + z1, z02 >= 0, z12 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z019), activate(z119))) + ACTIVATE(1 + z019 + z119) :|: z = 1 + z0 + (1 + z019 + z119), z019 >= 0, z119 >= 0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, fib1(activate(z09), activate(z19))) + ACTIVATE(z0) :|: z19 >= 0, z0 >= 0, z09 >= 0, z = 1 + z0 + (1 + z09 + z19) ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z010), activate(z110))) + ACTIVATE(z0) :|: z110 >= 0, z = 1 + z0 + (1 + z010 + z110), z0 >= 0, z010 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADD(0, add(activate(z020), activate(z120))) + ACTIVATE(1 + z020 + z120) :|: z120 >= 0, z0 >= 0, z = 1 + z0 + (1 + z020 + z120), z020 >= 0 ADD(z, z') -{ z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z - 1 >= 0 FIB(z) -{ 0 }-> 0 :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 0) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + 0)) :|: z >= 0 FIB(z) -{ 0 }-> 1 + SEL(z, 1 + (1 + 0) + (1 + (1 + 0) + (1 + (1 + 0) + (1 + 0)))) :|: z >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, fib1(activate(z0'), activate(z1'))) + ACTIVATE(1 + z0' + z1') :|: z' = 1 + z1 + (1 + z0' + z1'), z1 >= 0, z0' >= 0, z1' >= 0, z - 1 >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, add(activate(z0''), activate(z1''))) + ACTIVATE(1 + z0'' + z1'') :|: z' = 1 + z1 + (1 + z0'' + z1''), z1 >= 0, z - 1 >= 0, z0'' >= 0, z1'' >= 0 SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 activate(z) -{ 0 }-> s10 :|: s10 >= 0, s10 <= 0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s7 :|: s7 >= 0, s7 <= z0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s8 :|: s8 >= 0, s8 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> s9 :|: s9 >= 0, s9 <= 0 + z1 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> fib1(z0, fib1(activate(z027), activate(z127))) :|: z027 >= 0, z0 >= 0, z127 >= 0, z = 1 + z0 + (1 + z027 + z127) activate(z) -{ 0 }-> fib1(z0, add(activate(z028), activate(z128))) :|: z128 >= 0, z0 >= 0, z = 1 + z0 + (1 + z028 + z128), z028 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), z1) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), fib1(activate(z023), activate(z123))) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + (1 + z023 + z123), z121 >= 0, z123 >= 0, z023 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), add(activate(z024), activate(z124))) :|: z021 >= 0, z124 >= 0, z = 1 + (1 + z021 + z121) + (1 + z024 + z124), z121 >= 0, z024 >= 0 activate(z) -{ 0 }-> fib1(fib1(activate(z021), activate(z121)), 0) :|: z021 >= 0, z = 1 + (1 + z021 + z121) + z1, z1 >= 0, z121 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), z1) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), fib1(activate(z025), activate(z125))) :|: z025 >= 0, z = 1 + (1 + z022 + z122) + (1 + z025 + z125), z022 >= 0, z122 >= 0, z125 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), add(activate(z026), activate(z126))) :|: z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + (1 + z026 + z126), z026 >= 0, z126 >= 0 activate(z) -{ 0 }-> fib1(add(activate(z022), activate(z122)), 0) :|: z1 >= 0, z022 >= 0, z122 >= 0, z = 1 + (1 + z022 + z122) + z1 activate(z) -{ 0 }-> fib1(0, fib1(activate(z029), activate(z129))) :|: z029 >= 0, z129 >= 0, z = 1 + z0 + (1 + z029 + z129), z0 >= 0 activate(z) -{ 0 }-> fib1(0, add(activate(z030), activate(z130))) :|: z130 >= 0, z0 >= 0, z = 1 + z0 + (1 + z030 + z130), z030 >= 0 activate(z) -{ 0 }-> add(z0, fib1(activate(z037), activate(z137))) :|: z = 1 + z0 + (1 + z037 + z137), z0 >= 0, z137 >= 0, z037 >= 0 activate(z) -{ 0 }-> add(z0, add(activate(z038), activate(z138))) :|: z138 >= 0, z0 >= 0, z = 1 + z0 + (1 + z038 + z138), z038 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), z1) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), fib1(activate(z033), activate(z133))) :|: z031 >= 0, z131 >= 0, z133 >= 0, z033 >= 0, z = 1 + (1 + z031 + z131) + (1 + z033 + z133) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), add(activate(z034), activate(z134))) :|: z031 >= 0, z131 >= 0, z134 >= 0, z034 >= 0, z = 1 + (1 + z031 + z131) + (1 + z034 + z134) activate(z) -{ 0 }-> add(fib1(activate(z031), activate(z131)), 0) :|: z = 1 + (1 + z031 + z131) + z1, z031 >= 0, z131 >= 0, z1 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), z1) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), fib1(activate(z035), activate(z135))) :|: z032 >= 0, z035 >= 0, z132 >= 0, z = 1 + (1 + z032 + z132) + (1 + z035 + z135), z135 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), add(activate(z036), activate(z136))) :|: z032 >= 0, z036 >= 0, z = 1 + (1 + z032 + z132) + (1 + z036 + z136), z132 >= 0, z136 >= 0 activate(z) -{ 0 }-> add(add(activate(z032), activate(z132)), 0) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032 + z132) + z1, z132 >= 0 activate(z) -{ 0 }-> add(0, fib1(activate(z039), activate(z139))) :|: z039 >= 0, z139 >= 0, z0 >= 0, z = 1 + z0 + (1 + z039 + z139) activate(z) -{ 0 }-> add(0, add(activate(z040), activate(z140))) :|: z = 1 + z0 + (1 + z040 + z140), z040 >= 0, z0 >= 0, z140 >= 0 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, 0 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1 activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, 0 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + z1' + (1 + z0' + z1')) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 0 = z1', z0' >= 0 add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + z' + 1, z' >= 0, z - 1 >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 fib1(z, z') -{ 0 }-> 1 + z + (1 + z' + (1 + z + z')) :|: z' >= 0, z >= 0 Function symbols to be analyzed: {activate}, {ACTIVATE}, {SEL}, {FIB} Previous analysis results are: ADD: runtime: O(n^1) [z], size: O(1) [0] add: runtime: O(1) [0], size: O(n^1) [1 + z + z'] fib1: runtime: O(1) [0], size: O(n^1) [3 + 2*z + 2*z'] ---------------------------------------- (107) 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: FIB(v0) -> null_FIB [0] activate(v0) -> null_activate [0] fib1(v0, v1) -> null_fib1 [0] add(v0, v1) -> null_add [0] ADD(v0, v1) -> null_ADD [0] SEL(v0, v1) -> null_SEL [0] ACTIVATE(v0) -> null_ACTIVATE [0] And the following fresh constants: null_FIB, null_activate, null_fib1, null_add, null_ADD, null_SEL, null_ACTIVATE ---------------------------------------- (108) 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: ADD(s(z0), z1) -> c4(ADD(z0, z1)) [1] SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) [1] ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) [1] ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) [1] ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) [1] ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) [1] FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) [0] activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) [0] activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) [0] activate(z0) -> z0 [0] fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) [0] fib1(z0, z1) -> n__fib1(z0, z1) [0] add(0, z0) -> z0 [0] add(s(z0), z1) -> s(add(z0, z1)) [0] add(z0, z1) -> n__add(z0, z1) [0] FIB(v0) -> null_FIB [0] activate(v0) -> null_activate [0] fib1(v0, v1) -> null_fib1 [0] add(v0, v1) -> null_add [0] ADD(v0, v1) -> null_ADD [0] SEL(v0, v1) -> null_SEL [0] ACTIVATE(v0) -> null_ACTIVATE [0] The TRS has the following type information: ADD :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> c4:null_ADD s :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add c4 :: c4:null_ADD -> c4:null_ADD SEL :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> c7:null_SEL cons :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add c7 :: c7:null_SEL -> c10:c11:c8:c9:null_ACTIVATE -> c7:null_SEL activate :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add ACTIVATE :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> c10:c11:c8:c9:null_ACTIVATE n__add :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add c10 :: c4:null_ADD -> c10:c11:c8:c9:null_ACTIVATE -> c10:c11:c8:c9:null_ACTIVATE c11 :: c4:null_ADD -> c10:c11:c8:c9:null_ACTIVATE -> c10:c11:c8:c9:null_ACTIVATE n__fib1 :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add c8 :: c10:c11:c8:c9:null_ACTIVATE -> c10:c11:c8:c9:null_ACTIVATE c9 :: c10:c11:c8:c9:null_ACTIVATE -> c10:c11:c8:c9:null_ACTIVATE FIB :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> c:null_FIB c :: c7:null_SEL -> c:null_FIB fib1 :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add 0 :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add add :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add -> s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add null_FIB :: c:null_FIB null_activate :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add null_fib1 :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add null_add :: s:cons:n__add:n__fib1:0:null_activate:null_fib1:null_add null_ADD :: c4:null_ADD null_SEL :: c7:null_SEL null_ACTIVATE :: c10:c11:c8:c9:null_ACTIVATE Rewrite Strategy: INNERMOST ---------------------------------------- (109) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 null_FIB => 0 null_activate => 0 null_fib1 => 0 null_add => 0 null_ADD => 0 null_SEL => 0 null_ACTIVATE => 0 ---------------------------------------- (110) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(activate(z0), activate(z1)) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ACTIVATE(z) -{ 1 }-> 1 + ADD(activate(z0), activate(z1)) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADD(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 ADD(z, z') -{ 1 }-> 1 + ADD(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 FIB(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 FIB(z) -{ 0 }-> 1 + SEL(z0, fib1(1 + 0, 1 + 0)) :|: z = z0, z0 >= 0 SEL(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 SEL(z, z') -{ 1 }-> 1 + SEL(z0, activate(z2)) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> fib1(activate(z0), activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> add(activate(z0), activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 add(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 add(z, z') -{ 0 }-> 1 + add(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib1(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 fib1(z, z') -{ 0 }-> 1 + z0 + (1 + z1 + (1 + z0 + z1)) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (111) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) We considered the (Usable) Rules:none And the Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = [3] POL(ACTIVATE(x_1)) = 0 POL(ADD(x_1, x_2)) = 0 POL(FIB(x_1)) = [2] + x_1 POL(SEL(x_1, x_2)) = x_1 POL(activate(x_1)) = [3]x_1 POL(add(x_1, x_2)) = [3] POL(c(x_1)) = x_1 POL(c10(x_1, x_2)) = x_1 + x_2 POL(c11(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c7(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)) = [3] + x_1 + x_2 POL(fib1(x_1, x_2)) = 0 POL(n__add(x_1, x_2)) = 0 POL(n__fib1(x_1, x_2)) = x_2 POL(s(x_1)) = [1] + x_1 ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, SEL_2, ACTIVATE_1, FIB_1 Compound Symbols: c4_1, c7_2, c10_2, c11_2, c_1, c8_1, c9_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) by SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, FIB_1, SEL_2 Compound Symbols: c4_1, c10_2, c11_2, c_1, c8_1, c9_1, c7_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(z0, z1)) -> c10(ADD(activate(z0), activate(z1)), ACTIVATE(z0)) by ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, FIB_1, SEL_2 Compound Symbols: c4_1, c11_2, c_1, c8_1, c9_1, c7_2, c10_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(z0, z1)) -> c11(ADD(activate(z0), activate(z1)), ACTIVATE(z1)) by ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, FIB_1, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c_1, c8_1, c9_1, c7_2, c10_2, c11_2 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) by FIB(x0) -> c(SEL(x0, cons(s(0), n__fib1(s(0), n__add(s(0), s(0)))))) FIB(x0) -> c(SEL(x0, n__fib1(s(0), s(0)))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) FIB(x0) -> c(SEL(x0, cons(s(0), n__fib1(s(0), n__add(s(0), s(0)))))) FIB(x0) -> c(SEL(x0, n__fib1(s(0), s(0)))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples: FIB(z0) -> c(SEL(z0, fib1(s(0), s(0)))) SEL(s(z0), cons(z1, z2)) -> c7(SEL(z0, activate(z2)), ACTIVATE(z2)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2, FIB_1 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c_1 ---------------------------------------- (121) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: FIB(x0) -> c(SEL(x0, cons(s(0), n__fib1(s(0), n__add(s(0), s(0)))))) Removed 1 trailing nodes: FIB(x0) -> c(SEL(x0, n__fib1(s(0), s(0)))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SEL(s(x0), cons(x1, n__fib1(z0, z1))) -> c7(SEL(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) by SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, n__fib1(activate(x2), activate(x3))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, n__fib1(activate(x2), activate(x3))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SEL(s(x0), cons(x1, n__add(z0, z1))) -> c7(SEL(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) by SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(SEL(x0, n__add(activate(x2), activate(x3))), ACTIVATE(n__add(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(SEL(x0, n__add(activate(x2), activate(x3))), ACTIVATE(n__add(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(x0)) by ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(x0)) by ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(x0, z0)) -> c10(ADD(activate(x0), z0), ACTIVATE(x0)) by ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__fib1(z0, z1))) by ACTIVATE(n__add(n__fib1(x0, x1), n__fib1(z0, z1))) -> c10(ADD(fib1(activate(x0), activate(x1)), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), n__add(z0, z1))) -> c10(ADD(fib1(activate(x0), activate(x1)), add(activate(z0), activate(z1))), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), z0)) -> c10(ADD(fib1(activate(x0), activate(x1)), z0), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ADD(cons(activate(x0), n__fib1(activate(x1), n__add(activate(x0), activate(x1)))), activate(x2)), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ADD(n__fib1(activate(x0), activate(x1)), activate(x2)), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ADD(cons(activate(x0), n__fib1(activate(x1), n__add(activate(x0), activate(x1)))), activate(x2)), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ADD(n__fib1(activate(x0), activate(x1)), activate(x2)), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ADD(cons(activate(x0), n__fib1(activate(x1), n__add(activate(x0), activate(x1)))), activate(x2)), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ADD(n__fib1(activate(x0), activate(x1)), activate(x2)), ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1, c10_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(n__add(z0, z1))) by ACTIVATE(n__add(n__add(x0, x1), n__fib1(z0, z1))) -> c10(ADD(add(activate(x0), activate(x1)), fib1(activate(z0), activate(z1))), ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(n__add(x0, x1), n__add(z0, z1))) -> c10(ADD(add(activate(x0), activate(x1)), add(activate(z0), activate(z1))), ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(n__add(x0, x1), z0)) -> c10(ADD(add(activate(x0), activate(x1)), z0), ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ADD(n__add(activate(x0), activate(x1)), activate(x2)), ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ADD(n__add(activate(x0), activate(x1)), activate(x2)), ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ADD(n__add(activate(x0), activate(x1)), activate(x2)), ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1, c10_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c10_2, c11_2, c7_1, c10_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, activate(x1)), ACTIVATE(z0)) by ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c10(ADD(x0, fib1(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c10(ADD(x0, add(activate(z0), activate(z1))), ACTIVATE(x0)) ACTIVATE(n__add(x0, z0)) -> c10(ADD(x0, z0), ACTIVATE(x0)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(activate(x0), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) by ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(activate(x0), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) by ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(x0, z0)) -> c11(ADD(activate(x0), z0), ACTIVATE(z0)) by ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) by ACTIVATE(n__add(n__fib1(x0, x1), n__fib1(z0, z1))) -> c11(ADD(fib1(activate(x0), activate(x1)), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__fib1(x0, x1), n__add(z0, z1))) -> c11(ADD(fib1(activate(x0), activate(x1)), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__fib1(x0, x1), z0)) -> c11(ADD(fib1(activate(x0), activate(x1)), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ADD(cons(activate(x0), n__fib1(activate(x1), n__add(activate(x0), activate(x1)))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ADD(n__fib1(activate(x0), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ADD(cons(activate(x0), n__fib1(activate(x1), n__add(activate(x0), activate(x1)))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ADD(n__fib1(activate(x0), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ADD(cons(activate(x0), n__fib1(activate(x1), n__add(activate(x0), activate(x1)))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ADD(n__fib1(activate(x0), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1, c11_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), activate(x1)), ACTIVATE(x1)) by ACTIVATE(n__add(n__add(x0, x1), n__fib1(z0, z1))) -> c11(ADD(add(activate(x0), activate(x1)), fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(x0, x1), n__add(z0, z1))) -> c11(ADD(add(activate(x0), activate(x1)), add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__add(x0, x1), z0)) -> c11(ADD(add(activate(x0), activate(x1)), z0), ACTIVATE(z0)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ADD(n__add(activate(x0), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ADD(n__add(activate(x0), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ADD(n__add(activate(x0), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1, c11_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c11_2, c7_1, c10_2, c10_1, c11_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, activate(x1)), ACTIVATE(x1)) by ACTIVATE(n__add(x0, n__fib1(z0, z1))) -> c11(ADD(x0, fib1(activate(z0), activate(z1))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(x0, n__add(z0, z1))) -> c11(ADD(x0, add(activate(z0), activate(z1))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(x0, z0)) -> c11(ADD(x0, z0), ACTIVATE(z0)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) S tuples: ADD(s(z0), z1) -> c4(ADD(z0, z1)) ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ADD_2, ACTIVATE_1, SEL_2 Compound Symbols: c4_1, c8_1, c9_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (163) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ADD(s(z0), z1) -> c4(ADD(z0, z1)) by ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) S tuples: ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ACTIVATE_1, SEL_2, ADD_2 Compound Symbols: c8_1, c9_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1 ---------------------------------------- (165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__fib1(z0, z1)) -> c8(ACTIVATE(z0)) by ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) S tuples: ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: ACTIVATE_1, SEL_2, ADD_2 Compound Symbols: c9_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__fib1(z0, z1)) -> c9(ACTIVATE(z1)) by ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SEL(s(x0), cons(x1, z0)) -> c7(SEL(x0, z0), ACTIVATE(z0)) by SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2)), ACTIVATE(cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3))), ACTIVATE(cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4)))), ACTIVATE(cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4)))), ACTIVATE(cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4))), ACTIVATE(cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4))), ACTIVATE(cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4)))), ACTIVATE(cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4)))), ACTIVATE(cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3))), ACTIVATE(cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4))), ACTIVATE(cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4))), ACTIVATE(cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(SEL(z0, n__add(y0, n__fib1(y1, y2))), ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3)))), ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__fib1(y1, n__add(y2, y3)))), ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3))), ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__fib1(n__add(y1, y2), y3))), ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(SEL(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3))), ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(SEL(z0, n__add(n__add(y0, y1), n__fib1(y2, y3))), ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(SEL(z0, n__add(y0, n__add(y1, y2))), ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__add(y1, n__fib1(y2, y3)))), ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__add(y1, n__add(y2, y3)))), ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__add(n__fib1(y1, y2), y3))), ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__add(n__add(y1, y2), y3))), ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(SEL(z0, n__add(n__fib1(y0, y1), n__add(y2, y3))), ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(SEL(z0, n__add(n__add(y0, y1), n__add(y2, y3))), ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(SEL(z0, n__add(n__fib1(y0, y1), y2)), ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(SEL(z0, n__add(n__add(y0, y1), y2)), ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(y0, y1))) -> c7(SEL(z0, n__add(y0, y1)), ACTIVATE(n__add(y0, y1))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3)), ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3)), ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3)), ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__fib1(n__add(y0, y1), y2), y3)), ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3)), ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__add(y0, n__add(y1, y2)), y3)), ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__add(n__fib1(y0, y1), y2), y3)), ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__add(n__add(y0, y1), y2), y3)), ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(SEL(z0, n__fib1(n__fib1(y0, y1), y2)), ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3)), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3)), ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3)), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, y1), y2), y3)), ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(SEL(z0, n__fib1(n__add(y0, y1), y2)), ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(y1, y2))), ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(y2, y3)))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(y2, y3)))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, y2))), ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2)), ACTIVATE(cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3))), ACTIVATE(cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4)))), ACTIVATE(cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4)))), ACTIVATE(cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4))), ACTIVATE(cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4))), ACTIVATE(cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4)))), ACTIVATE(cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4)))), ACTIVATE(cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3))), ACTIVATE(cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4))), ACTIVATE(cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4))), ACTIVATE(cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(SEL(z0, n__add(y0, n__fib1(y1, y2))), ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3)))), ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__fib1(y1, n__add(y2, y3)))), ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3))), ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__fib1(n__add(y1, y2), y3))), ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(SEL(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3))), ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(SEL(z0, n__add(n__add(y0, y1), n__fib1(y2, y3))), ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(SEL(z0, n__add(y0, n__add(y1, y2))), ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__add(y1, n__fib1(y2, y3)))), ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(SEL(z0, n__add(y0, n__add(y1, n__add(y2, y3)))), ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__add(n__fib1(y1, y2), y3))), ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__add(y0, n__add(n__add(y1, y2), y3))), ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(SEL(z0, n__add(n__fib1(y0, y1), n__add(y2, y3))), ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(SEL(z0, n__add(n__add(y0, y1), n__add(y2, y3))), ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(SEL(z0, n__add(n__fib1(y0, y1), y2)), ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(SEL(z0, n__add(n__add(y0, y1), y2)), ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(y0, y1))) -> c7(SEL(z0, n__add(y0, y1)), ACTIVATE(n__add(y0, y1))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3)), ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3)), ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3)), ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__fib1(n__add(y0, y1), y2), y3)), ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3)), ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(SEL(z0, n__add(n__add(y0, n__add(y1, y2)), y3)), ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__add(n__fib1(y0, y1), y2), y3)), ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(SEL(z0, n__add(n__add(n__add(y0, y1), y2), y3)), ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(SEL(z0, n__fib1(n__fib1(y0, y1), y2)), ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3)), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3)), ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4)), ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3)), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, y1), y2), y3)), ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(SEL(z0, n__fib1(n__add(y0, y1), y2)), ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(SEL(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4)), ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(y1, y2))), ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(y2, y3)))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(y2, y3)))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4))))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4)))), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4)))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(SEL(z0, n__fib1(y0, n__add(y1, y2))), ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(y1, y2), y3))), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(SEL(z0, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5))), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 114 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (173) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(ACTIVATE(n__fib1(x2, x3))) by SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), z3))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), z3))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z3))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(z2, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(z2, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(z2, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (175) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) by ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, y2)), z1), ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1), ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1), ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ADD(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1), ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ADD(n__add(y0, n__add(y1, y2)), z1), ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__add(y1, n__add(y2, y3))), z1), ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__add(n__add(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1), ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ADD(n__add(n__add(y0, y1), n__add(y2, y3)), z1), ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), y2), z1), ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ADD(n__add(n__add(y0, y1), y2), z1), ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(y0, y1), z1)) -> c10(ADD(n__add(y0, y1), z1), ACTIVATE(n__add(y0, y1))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__fib1(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__add(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__add(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__add(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1), ACTIVATE(s(s(y0)))) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ADD(n__fib1(n__fib1(y0, y1), y2), z1), ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ADD(n__fib1(n__add(y0, y1), y2), z1), ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(y1, y2)), z1), ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, y2)), z1), ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, y2)), z1), ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1), ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1), ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ADD(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1), ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ADD(n__add(y0, n__add(y1, y2)), z1), ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__add(y1, n__add(y2, y3))), z1), ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__add(n__add(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1), ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ADD(n__add(n__add(y0, y1), n__add(y2, y3)), z1), ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), y2), z1), ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ADD(n__add(n__add(y0, y1), y2), z1), ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(y0, y1), z1)) -> c10(ADD(n__add(y0, y1), z1), ACTIVATE(n__add(y0, y1))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__fib1(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__add(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__add(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__add(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1), ACTIVATE(s(s(y0)))) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ADD(n__fib1(n__fib1(y0, y1), y2), z1), ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ADD(n__fib1(n__add(y0, y1), y2), z1), ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(y1, y2)), z1), ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, y2)), z1), ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, y2)), z1), ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1), ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1), ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ADD(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1), ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ADD(n__add(y0, n__add(y1, y2)), z1), ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__add(y0, n__add(y1, n__add(y2, y3))), z1), ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__add(y0, n__add(n__add(y1, y2), y3)), z1), ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1), ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ADD(n__add(n__add(y0, y1), n__add(y2, y3)), z1), ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ADD(n__add(n__fib1(y0, y1), y2), z1), ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ADD(n__add(n__add(y0, y1), y2), z1), ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(y0, y1), z1)) -> c10(ADD(n__add(y0, y1), z1), ACTIVATE(n__add(y0, y1))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__fib1(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__add(n__add(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__add(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__add(n__add(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1), ACTIVATE(s(s(y0)))) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ADD(n__fib1(n__fib1(y0, y1), y2), z1), ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1), ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, y1), y2), y3), z1), ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ADD(n__fib1(n__add(y0, y1), y2), z1), ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ADD(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1), ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(y1, y2)), z1), ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1), ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ADD(n__fib1(y0, n__add(y1, y2)), z1), ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ADD(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1), ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 104 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) K tuples:none Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (179) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) We considered the (Usable) Rules:none And the Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(ACTIVATE(x_1)) = [1] POL(ADD(x_1, x_2)) = 0 POL(SEL(x_1, x_2)) = [1] + x_1 POL(activate(x_1)) = 0 POL(add(x_1, x_2)) = 0 POL(c10(x_1)) = x_1 POL(c10(x_1, x_2)) = x_1 + x_2 POL(c11(x_1)) = x_1 POL(c11(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c7(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(fib1(x_1, x_2)) = 0 POL(n__add(x_1, x_2)) = 0 POL(n__fib1(x_1, x_2)) = 0 POL(s(x_1)) = [1] + x_1 ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) K tuples: ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (181) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) by ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), z1), z2)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(z0, n__fib1(y1, y2)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(y2, y3))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(y2, y3))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(y2, n__add(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(n__add(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, y2), n__add(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, y2)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, n__add(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(n__add(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__fib1(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) K tuples: ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1 ---------------------------------------- (183) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c10(ACTIVATE(n__fib1(x0, x1))) by ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), z1), z2)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1), z2)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1))) ACTIVATE(n__add(n__fib1(z0, n__fib1(y1, y2)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(y2, y3))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(y2, y3))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(y2, n__add(y3, y4)))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, n__add(n__add(y2, y3), y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, y2), n__add(y3, y4))), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__add(y1, y2)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(y1, n__add(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__add(n__add(n__add(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__fib1(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(y1, y2), y3)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(z0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z2)) -> c10(ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__fib1(z0, z1)) -> fib1(activate(z0), activate(z1)) activate(n__add(z0, z1)) -> add(activate(z0), activate(z1)) activate(z0) -> z0 fib1(z0, z1) -> cons(z0, n__fib1(z1, n__add(z0, z1))) fib1(z0, z1) -> n__fib1(z0, z1) add(0, z0) -> z0 add(s(z0), z1) -> s(add(z0, z1)) add(z0, z1) -> n__add(z0, z1) Tuples: SEL(s(x0), cons(x1, n__fib1(x2, x3))) -> c7(SEL(x0, cons(activate(x2), n__fib1(activate(x3), n__add(activate(x2), activate(x3))))), ACTIVATE(n__fib1(x2, x3))) SEL(s(x0), cons(x1, n__fib1(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, n__add(z0, z1)))) -> c7(SEL(x0, fib1(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__fib1(x2, z0))) -> c7(SEL(x0, fib1(activate(x2), z0)), ACTIVATE(n__fib1(x2, z0))) SEL(s(x0), cons(x1, n__fib1(n__fib1(z0, z1), x3))) -> c7(SEL(x0, fib1(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(n__add(z0, z1), x3))) -> c7(SEL(x0, fib1(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__fib1(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__fib1(z0, x3))) -> c7(SEL(x0, fib1(z0, activate(x3))), ACTIVATE(n__fib1(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, n__fib1(z0, z1)))) -> c7(SEL(x0, add(activate(x2), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__fib1(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, n__add(z0, z1)))) -> c7(SEL(x0, add(activate(x2), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x2, n__add(z0, z1)))) SEL(s(x0), cons(x1, n__add(x2, z0))) -> c7(SEL(x0, add(activate(x2), z0)), ACTIVATE(n__add(x2, z0))) SEL(s(x0), cons(x1, n__add(n__fib1(z0, z1), x3))) -> c7(SEL(x0, add(fib1(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__fib1(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(n__add(z0, z1), x3))) -> c7(SEL(x0, add(add(activate(z0), activate(z1)), activate(x3))), ACTIVATE(n__add(n__add(z0, z1), x3))) SEL(s(x0), cons(x1, n__add(z0, x3))) -> c7(SEL(x0, add(z0, activate(x3))), ACTIVATE(n__add(z0, x3))) SEL(s(x0), cons(x1, n__add(x2, x3))) -> c7(ACTIVATE(n__add(x2, x3))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, x1)) -> c10(ADD(z0, x1), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c7(SEL(s(y0), cons(y1, y2))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__fib1(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__fib1(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__fib1(n__add(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__fib1(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__fib1(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, n__add(y3, y4))))) -> c7(SEL(s(y0), cons(y1, n__add(y2, n__add(y3, y4))))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(y2, y3)))) -> c7(SEL(s(y0), cons(y1, n__add(y2, y3)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__fib1(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__fib1(y2, y3), y4)))) SEL(s(s(y0)), cons(z1, cons(y1, n__add(n__add(y2, y3), y4)))) -> c7(SEL(s(y0), cons(y1, n__add(n__add(y2, y3), y4)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__add(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c7(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__add(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__add(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__fib1(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) SEL(s(z0), cons(z1, n__fib1(n__add(y0, y1), y2))) -> c7(ACTIVATE(n__fib1(n__add(y0, y1), y2))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c7(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, y3))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(y1, y2)))) -> c7(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) SEL(s(z0), cons(z1, n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) -> c7(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) S tuples: ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c10(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c10(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c10(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c10(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c10(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c10(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c10(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c10(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c10(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c10(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(x0)) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c10(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c10(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c10(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(z0)) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c10(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(n__fib1(z0, z1))) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c10(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(n__add(z0, z1))) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c10(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__fib1(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c10(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(n__fib1(x0, z0))) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c10(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c10(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__fib1(n__add(z0, z1), x1))) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c10(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(n__fib1(z0, x1))) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c10(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__fib1(z0, z1)))) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c10(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(n__add(x0, n__add(z0, z1)))) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c10(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(n__add(x0, z0))) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c10(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__fib1(z0, z1), x1))) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c10(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(n__add(n__add(z0, z1), x1))) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c10(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(n__add(z0, x1))) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c10(ACTIVATE(n__add(x0, x1))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), cons(activate(x1), n__fib1(activate(x2), n__add(activate(x1), activate(x2))))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, x2))) -> c11(ADD(activate(x0), n__fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__fib1(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), fib1(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__fib1(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__fib1(x1, z0))) -> c11(ADD(activate(x0), fib1(activate(x1), z0)), ACTIVATE(n__fib1(x1, z0))) ACTIVATE(n__add(x0, n__fib1(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), fib1(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__fib1(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__fib1(z0, x2))) -> c11(ADD(activate(x0), fib1(z0, activate(x2))), ACTIVATE(n__fib1(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__fib1(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__fib1(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(z0, n__fib1(x1, x2))) -> c11(ADD(z0, fib1(activate(x1), activate(x2))), ACTIVATE(n__fib1(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, x2))) -> c11(ADD(activate(x0), n__add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(x0, n__add(x1, n__fib1(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), fib1(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__fib1(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, n__add(z0, z1)))) -> c11(ADD(activate(x0), add(activate(x1), add(activate(z0), activate(z1)))), ACTIVATE(n__add(x1, n__add(z0, z1)))) ACTIVATE(n__add(x0, n__add(x1, z0))) -> c11(ADD(activate(x0), add(activate(x1), z0)), ACTIVATE(n__add(x1, z0))) ACTIVATE(n__add(x0, n__add(n__fib1(z0, z1), x2))) -> c11(ADD(activate(x0), add(fib1(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__fib1(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(n__add(z0, z1), x2))) -> c11(ADD(activate(x0), add(add(activate(z0), activate(z1)), activate(x2))), ACTIVATE(n__add(n__add(z0, z1), x2))) ACTIVATE(n__add(x0, n__add(z0, x2))) -> c11(ADD(activate(x0), add(z0, activate(x2))), ACTIVATE(n__add(z0, x2))) ACTIVATE(n__add(n__fib1(z0, z1), n__add(x1, x2))) -> c11(ADD(fib1(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__add(z0, z1), n__add(x1, x2))) -> c11(ADD(add(activate(z0), activate(z1)), add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(z0, n__add(x1, x2))) -> c11(ADD(z0, add(activate(x1), activate(x2))), ACTIVATE(n__add(x1, x2))) ACTIVATE(n__add(n__fib1(z0, z1), x1)) -> c11(ADD(fib1(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(n__add(z0, z1), x1)) -> c11(ADD(add(activate(z0), activate(z1)), x1), ACTIVATE(x1)) ACTIVATE(n__add(z0, x1)) -> c11(ADD(z0, x1), ACTIVATE(x1)) ACTIVATE(n__add(n__fib1(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, n__add(z0, z1)), x2)) -> c11(ADD(fib1(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, z0), x2)) -> c11(ADD(fib1(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__fib1(z0, z1), x1), x2)) -> c11(ADD(fib1(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(n__add(z0, z1), x1), x2)) -> c11(ADD(fib1(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(z0, x1), x2)) -> c11(ADD(fib1(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__fib1(x0, x1), x2)) -> c11(ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__fib1(z0, z1)), x2)) -> c11(ADD(add(activate(x0), fib1(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, n__add(z0, z1)), x2)) -> c11(ADD(add(activate(x0), add(activate(z0), activate(z1))), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, z0), x2)) -> c11(ADD(add(activate(x0), z0), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__fib1(z0, z1), x1), x2)) -> c11(ADD(add(fib1(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(n__add(z0, z1), x1), x2)) -> c11(ADD(add(add(activate(z0), activate(z1)), activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(z0, x1), x2)) -> c11(ADD(add(z0, activate(x1)), activate(x2)), ACTIVATE(x2)) ACTIVATE(n__add(n__add(x0, x1), x2)) -> c11(ACTIVATE(x2)) ADD(s(s(y0)), z1) -> c4(ADD(s(y0), z1)) ACTIVATE(n__fib1(n__fib1(y0, y1), z1)) -> c8(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c8(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c8(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), z1)) -> c8(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(n__add(y0, y1), z1)) -> c8(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c8(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c8(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(y0, y1))) -> c9(ACTIVATE(n__fib1(y0, y1))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__fib1(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__fib1(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, y2)))) -> c9(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__fib1(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(y1, n__add(y2, y3))))) -> c9(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__fib1(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(y0, n__add(n__add(y1, y2), y3)))) -> c9(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), n__add(y2, y3)))) -> c9(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__add(y0, y1))) -> c9(ACTIVATE(n__add(y0, y1))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__fib1(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__add(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__fib1(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, y2)), y3))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, y1), y2), y3))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__fib1(z0, n__fib1(n__add(y0, y1), y2))) -> c9(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__fib1(z0, n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) -> c9(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__fib1(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__fib1(y2, y3)))) ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__add(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__add(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__add(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__add(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__add(y0, y1), n__add(y2, y3)), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), n__add(y2, y3)))) ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__add(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__add(n__add(y0, y1), y2))) ACTIVATE(n__add(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__fib1(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__fib1(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__add(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__add(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__add(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__add(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__fib1(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__fib1(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__fib1(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__fib1(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, y2)), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, y2)), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__fib1(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(y1, n__add(y2, y3))), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__fib1(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, n__add(n__add(y1, y2), y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), n__add(y2, y3)), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, y1), y2), y3), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, y1), y2), y3))) ACTIVATE(n__add(n__fib1(n__add(y0, y1), y2), z1)) -> c10(ACTIVATE(n__fib1(n__add(y0, y1), y2))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__fib1(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__fib1(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(y0, n__add(y1, y2)), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__fib1(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4), z1)) -> c10(ACTIVATE(n__fib1(n__add(n__add(n__add(y0, y1), y2), y3), y4))) ACTIVATE(n__add(n__fib1(y0, n__fib1(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__fib1(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__fib1(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, y3))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, y3))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__fib1(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(y2, n__add(y3, y4)))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__fib1(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, n__add(n__add(y2, y3), y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), n__add(y3, y4))))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__add(y1, y2)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(y1, y2)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__fib1(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__add(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__fib1(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__fib1(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__fib1(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, y3)), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__fib1(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(y2, n__add(y3, y4))), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__fib1(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, n__add(n__add(y2, y3), y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), n__add(y3, y4)), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, y2), y3), y4)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(y1, y2), y3)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(y1, y2), y3)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__fib1(n__add(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__fib1(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(y1, n__add(y2, y3)), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__fib1(y1, y2), y3), y4), y5)))) ACTIVATE(n__add(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)), z1)) -> c10(ACTIVATE(n__fib1(y0, n__fib1(n__add(n__add(n__add(y1, y2), y3), y4), y5)))) K tuples: ACTIVATE(n__add(s(s(y0)), z1)) -> c10(ADD(s(s(y0)), z1)) Defined Rule Symbols: activate_1, fib1_2, add_2 Defined Pair Symbols: SEL_2, ACTIVATE_1, ADD_2 Compound Symbols: c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c4_1, c8_1, c9_1