/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 383 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 3978 ms] (12) BOUNDS(1, INF) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1180 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (40) CdtProblem (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (44) CdtProblem (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 49 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (48) CdtProblem (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtLeafRemovalProof [ComplexityIfPolyImplication, 4 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 17 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 126 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (164) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0) -> active(0) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) 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: active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0) -> active(0) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0) -> active(0) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) 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: active(fib(N)) -> mark(sel(N, fib1(s(0'), s(0')))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0', X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0', cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0') -> active(0') mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Innermost TRS: Rules: active(fib(N)) -> mark(sel(N, fib1(s(0'), s(0')))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0', X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0', cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0') -> active(0') mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) encArg(0') -> 0' encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) Types: active :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add mark :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add sel :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib1 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add s :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add 0' :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add add :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encArg :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_active :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_mark :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_sel :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib1 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_s :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_cons :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_add :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_active :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_mark :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_sel :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib1 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_s :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_0 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_cons :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_add :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add hole_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add1_3 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3 :: Nat -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add ---------------------------------------- (9) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: active, mark, sel, fib1, s, cons, add, fib, encArg They will be analysed ascendingly in the following order: active = mark sel < active fib1 < active s < active cons < active add < active active < encArg sel < mark fib1 < mark s < mark cons < mark add < mark fib < mark mark < encArg sel < encArg fib1 < encArg s < encArg cons < encArg add < encArg fib < encArg ---------------------------------------- (10) Obligation: Innermost TRS: Rules: active(fib(N)) -> mark(sel(N, fib1(s(0'), s(0')))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0', X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0', cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0') -> active(0') mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) encArg(0') -> 0' encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) Types: active :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add mark :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add sel :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib1 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add s :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add 0' :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add add :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encArg :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_active :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_mark :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_sel :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib1 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_s :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_cons :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_add :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_active :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_mark :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_sel :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib1 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_s :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_0 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_cons :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_add :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add hole_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add1_3 :: 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3 :: Nat -> 0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add Generator Equations: gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(0) <=> 0' gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(+(x, 1)) <=> cons_active(gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(x)) The following defined symbols remain to be analysed: sel, active, mark, fib1, s, cons, add, fib, encArg They will be analysed ascendingly in the following order: active = mark sel < active fib1 < active s < active cons < active add < active active < encArg sel < mark fib1 < mark s < mark cons < mark add < mark fib < mark mark < encArg sel < encArg fib1 < encArg s < encArg cons < encArg add < encArg fib < encArg ---------------------------------------- (11) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(+(1, n1419_3))) -> *3_3, rt in Omega(0) Induction Base: encArg(gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(+(1, 0))) Induction Step: encArg(gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(+(1, +(n1419_3, 1)))) ->_R^Omega(0) active(encArg(gen_0':cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add2_3(+(1, n1419_3)))) ->_IH active(*3_3) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (12) BOUNDS(1, INF) ---------------------------------------- (13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (14) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0) -> active(0) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) 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: active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(fib(X)) -> active(fib(mark(X))) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) mark(s(X)) -> active(s(mark(X))) mark(0) -> active(0) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) fib(mark(X)) -> fib(X) fib(active(X)) -> fib(X) sel(mark(X1), X2) -> sel(X1, X2) sel(X1, mark(X2)) -> sel(X1, X2) sel(active(X1), X2) -> sel(X1, X2) sel(X1, active(X2)) -> sel(X1, X2) fib1(mark(X1), X2) -> fib1(X1, X2) fib1(X1, mark(X2)) -> fib1(X1, X2) fib1(active(X1), X2) -> fib1(X1, X2) fib1(X1, active(X2)) -> fib1(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (17) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (18) 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: mark(0) -> active(0) active(c_sel(0, c_cons(X, XS))) -> mark(X) mark(c_fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) add(c_active(X1), X2) -> add(X1, X2) fib(c_mark(X)) -> fib(X) fib1(X1, c_mark(X2)) -> fib1(X1, X2) add(X1, c_mark(X2)) -> add(X1, X2) mark(c_s(X)) -> active(s(mark(X))) mark(c_add(X1, X2)) -> active(add(mark(X1), mark(X2))) s(c_active(X)) -> s(X) cons(c_mark(X1), X2) -> cons(X1, X2) mark(c_fib(X)) -> active(fib(mark(X))) sel(c_active(X1), X2) -> sel(X1, X2) fib1(c_active(X1), X2) -> fib1(X1, X2) active(c_fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) fib1(X1, c_active(X2)) -> fib1(X1, X2) cons(X1, c_active(X2)) -> cons(X1, X2) active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) cons(X1, c_mark(X2)) -> cons(X1, X2) fib1(c_mark(X1), X2) -> fib1(X1, X2) add(c_mark(X1), X2) -> add(X1, X2) fib(c_active(X)) -> fib(X) add(X1, c_active(X2)) -> add(X1, X2) s(c_mark(X)) -> s(X) active(c_add(c_s(X), Y)) -> mark(s(add(X, Y))) mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) sel(c_mark(X1), X2) -> sel(X1, X2) active(c_add(0, X)) -> mark(X) cons(c_active(X1), X2) -> cons(X1, X2) mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) sel(X1, c_active(X2)) -> sel(X1, X2) sel(X1, c_mark(X2)) -> sel(X1, X2) active(c_sel(c_s(N), c_cons(X, XS))) -> mark(sel(N, XS)) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_fib(x_1)) -> fib(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_fib(x_1) -> fib(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) s(x0) -> c_s(x0) active(x0) -> c_active(x0) fib1(x0, x1) -> c_fib1(x0, x1) fib(x0) -> c_fib(x0) add(x0, x1) -> c_add(x0, x1) cons(x0, x1) -> c_cons(x0, x1) sel(x0, x1) -> c_sel(x0, x1) mark(x0) -> c_mark(x0) Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) 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: mark(0) -> active(0) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) [1] add(c_active(X1), X2) -> add(X1, X2) [1] fib(c_mark(X)) -> fib(X) [1] fib1(X1, c_mark(X2)) -> fib1(X1, X2) [1] add(X1, c_mark(X2)) -> add(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_add(X1, X2)) -> active(add(mark(X1), mark(X2))) [1] s(c_active(X)) -> s(X) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] mark(c_fib(X)) -> active(fib(mark(X))) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] fib1(c_active(X1), X2) -> fib1(X1, X2) [1] active(c_fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) [1] fib1(X1, c_active(X2)) -> fib1(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] fib1(c_mark(X1), X2) -> fib1(X1, X2) [1] add(c_mark(X1), X2) -> add(X1, X2) [1] fib(c_active(X)) -> fib(X) [1] add(X1, c_active(X2)) -> add(X1, X2) [1] s(c_mark(X)) -> s(X) [1] active(c_add(c_s(X), Y)) -> mark(s(add(X, Y))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] active(c_add(0, X)) -> mark(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] sel(X1, c_active(X2)) -> sel(X1, X2) [1] sel(X1, c_mark(X2)) -> sel(X1, X2) [1] active(c_sel(c_s(N), c_cons(X, XS))) -> mark(sel(N, XS)) [1] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_fib(x_1)) -> fib(encArg(x_1)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_fib(x_1) -> fib(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] fib1(x0, x1) -> c_fib1(x0, x1) [0] fib(x0) -> c_fib(x0) [0] add(x0, x1) -> c_add(x0, x1) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] mark(x0) -> c_mark(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(0) -> active(0) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) [1] add(c_active(X1), X2) -> add(X1, X2) [1] fib(c_mark(X)) -> fib(X) [1] fib1(X1, c_mark(X2)) -> fib1(X1, X2) [1] add(X1, c_mark(X2)) -> add(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_add(X1, X2)) -> active(add(mark(X1), mark(X2))) [1] s(c_active(X)) -> s(X) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] mark(c_fib(X)) -> active(fib(mark(X))) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] fib1(c_active(X1), X2) -> fib1(X1, X2) [1] active(c_fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) [1] fib1(X1, c_active(X2)) -> fib1(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] fib1(c_mark(X1), X2) -> fib1(X1, X2) [1] add(c_mark(X1), X2) -> add(X1, X2) [1] fib(c_active(X)) -> fib(X) [1] add(X1, c_active(X2)) -> add(X1, X2) [1] s(c_mark(X)) -> s(X) [1] active(c_add(c_s(X), Y)) -> mark(s(add(X, Y))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] active(c_add(0, X)) -> mark(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] sel(X1, c_active(X2)) -> sel(X1, X2) [1] sel(X1, c_mark(X2)) -> sel(X1, X2) [1] active(c_sel(c_s(N), c_cons(X, XS))) -> mark(sel(N, XS)) [1] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_fib(x_1)) -> fib(encArg(x_1)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_fib(x_1) -> fib(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] fib1(x0, x1) -> c_fib1(x0, x1) [0] fib(x0) -> c_fib(x0) [0] add(x0, x1) -> c_add(x0, x1) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] mark(x0) -> c_mark(x0) [0] The TRS has the following type information: mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add 0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encArg :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add Rewrite Strategy: INNERMOST ---------------------------------------- (23) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_active_1 encode_fib_1 encode_mark_1 encode_sel_2 encode_fib1_2 encode_s_1 encode_0 encode_cons_2 encode_add_2 s_1 active_1 fib1_2 fib_1 add_2 cons_2 sel_2 mark_1 Due to the following rules being added: encArg(v0) -> 0 [0] encode_active(v0) -> 0 [0] encode_fib(v0) -> 0 [0] encode_mark(v0) -> 0 [0] encode_sel(v0, v1) -> 0 [0] encode_fib1(v0, v1) -> 0 [0] encode_s(v0) -> 0 [0] encode_0 -> 0 [0] encode_cons(v0, v1) -> 0 [0] encode_add(v0, v1) -> 0 [0] s(v0) -> 0 [0] active(v0) -> 0 [0] fib1(v0, v1) -> 0 [0] fib(v0) -> 0 [0] add(v0, v1) -> 0 [0] cons(v0, v1) -> 0 [0] sel(v0, v1) -> 0 [0] mark(v0) -> 0 [0] And the following fresh constants: none ---------------------------------------- (24) 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: mark(0) -> active(0) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) [1] add(c_active(X1), X2) -> add(X1, X2) [1] fib(c_mark(X)) -> fib(X) [1] fib1(X1, c_mark(X2)) -> fib1(X1, X2) [1] add(X1, c_mark(X2)) -> add(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_add(X1, X2)) -> active(add(mark(X1), mark(X2))) [1] s(c_active(X)) -> s(X) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] mark(c_fib(X)) -> active(fib(mark(X))) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] fib1(c_active(X1), X2) -> fib1(X1, X2) [1] active(c_fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) [1] fib1(X1, c_active(X2)) -> fib1(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] fib1(c_mark(X1), X2) -> fib1(X1, X2) [1] add(c_mark(X1), X2) -> add(X1, X2) [1] fib(c_active(X)) -> fib(X) [1] add(X1, c_active(X2)) -> add(X1, X2) [1] s(c_mark(X)) -> s(X) [1] active(c_add(c_s(X), Y)) -> mark(s(add(X, Y))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] active(c_add(0, X)) -> mark(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] sel(X1, c_active(X2)) -> sel(X1, X2) [1] sel(X1, c_mark(X2)) -> sel(X1, X2) [1] active(c_sel(c_s(N), c_cons(X, XS))) -> mark(sel(N, XS)) [1] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_fib(x_1)) -> fib(encArg(x_1)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_fib(x_1) -> fib(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] fib1(x0, x1) -> c_fib1(x0, x1) [0] fib(x0) -> c_fib(x0) [0] add(x0, x1) -> c_add(x0, x1) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> 0 [0] encode_active(v0) -> 0 [0] encode_fib(v0) -> 0 [0] encode_mark(v0) -> 0 [0] encode_sel(v0, v1) -> 0 [0] encode_fib1(v0, v1) -> 0 [0] encode_s(v0) -> 0 [0] encode_0 -> 0 [0] encode_cons(v0, v1) -> 0 [0] encode_add(v0, v1) -> 0 [0] s(v0) -> 0 [0] active(v0) -> 0 [0] fib1(v0, v1) -> 0 [0] fib(v0) -> 0 [0] add(v0, v1) -> 0 [0] cons(v0, v1) -> 0 [0] sel(v0, v1) -> 0 [0] mark(v0) -> 0 [0] The TRS has the following type information: mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add 0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encArg :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add Rewrite Strategy: INNERMOST ---------------------------------------- (25) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (26) 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: mark(0) -> active(0) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) [1] add(c_active(X1), X2) -> add(X1, X2) [1] fib(c_mark(X)) -> fib(X) [1] fib1(X1, c_mark(X2)) -> fib1(X1, X2) [1] add(X1, c_mark(X2)) -> add(X1, X2) [1] mark(c_s(0)) -> active(s(active(0))) [2] mark(c_s(c_fib1(X139, X239))) -> active(s(active(fib1(mark(X139), mark(X239))))) [2] mark(c_s(c_s(X39))) -> active(s(active(s(mark(X39))))) [2] mark(c_s(c_add(X140, X240))) -> active(s(active(add(mark(X140), mark(X240))))) [2] mark(c_s(c_fib(X40))) -> active(s(active(fib(mark(X40))))) [2] mark(c_s(c_sel(X141, X241))) -> active(s(active(sel(mark(X141), mark(X241))))) [2] mark(c_s(c_cons(X142, X242))) -> active(s(active(cons(mark(X142), X242)))) [2] mark(c_s(X)) -> active(s(c_mark(X))) [1] mark(c_s(X)) -> active(s(0)) [1] mark(c_add(X1, X2)) -> active(add(mark(X1), mark(X2))) [1] s(c_active(X)) -> s(X) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] mark(c_fib(0)) -> active(fib(active(0))) [2] mark(c_fib(c_fib1(X183, X283))) -> active(fib(active(fib1(mark(X183), mark(X283))))) [2] mark(c_fib(c_s(X61))) -> active(fib(active(s(mark(X61))))) [2] mark(c_fib(c_add(X184, X284))) -> active(fib(active(add(mark(X184), mark(X284))))) [2] mark(c_fib(c_fib(X62))) -> active(fib(active(fib(mark(X62))))) [2] mark(c_fib(c_sel(X185, X285))) -> active(fib(active(sel(mark(X185), mark(X285))))) [2] mark(c_fib(c_cons(X186, X286))) -> active(fib(active(cons(mark(X186), X286)))) [2] mark(c_fib(X)) -> active(fib(c_mark(X))) [1] mark(c_fib(X)) -> active(fib(0)) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] fib1(c_active(X1), X2) -> fib1(X1, X2) [1] active(c_fib(N)) -> mark(sel(N, fib1(c_s(0), c_s(0)))) [1] active(c_fib(N)) -> mark(sel(N, fib1(c_s(0), 0))) [1] active(c_fib(N)) -> mark(sel(N, fib1(0, c_s(0)))) [1] active(c_fib(N)) -> mark(sel(N, fib1(0, 0))) [1] fib1(X1, c_active(X2)) -> fib1(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] active(c_fib1(c_active(X187), Y)) -> mark(cons(c_active(X187), fib1(Y, add(X187, Y)))) [2] active(c_fib1(X, c_mark(X287))) -> mark(cons(X, fib1(c_mark(X287), add(X, X287)))) [2] active(c_fib1(c_mark(X188), Y)) -> mark(cons(c_mark(X188), fib1(Y, add(X188, Y)))) [2] active(c_fib1(X, c_active(X288))) -> mark(cons(X, fib1(c_active(X288), add(X, X288)))) [2] active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, c_add(X, Y)))) [1] active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, 0))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] fib1(c_mark(X1), X2) -> fib1(X1, X2) [1] add(c_mark(X1), X2) -> add(X1, X2) [1] fib(c_active(X)) -> fib(X) [1] add(X1, c_active(X2)) -> add(X1, X2) [1] s(c_mark(X)) -> s(X) [1] active(c_add(c_s(c_active(X189)), Y)) -> mark(s(add(X189, Y))) [2] active(c_add(c_s(X), c_mark(X289))) -> mark(s(add(X, X289))) [2] active(c_add(c_s(c_mark(X190)), Y)) -> mark(s(add(X190, Y))) [2] active(c_add(c_s(X), c_active(X290))) -> mark(s(add(X, X290))) [2] active(c_add(c_s(X), Y)) -> mark(s(c_add(X, Y))) [1] active(c_add(c_s(X), Y)) -> mark(s(0)) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] active(c_add(0, X)) -> mark(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(0, X2)) -> active(cons(active(0), X2)) [2] mark(c_cons(c_fib1(X1131, X2131), X2)) -> active(cons(active(fib1(mark(X1131), mark(X2131))), X2)) [2] mark(c_cons(c_s(X83), X2)) -> active(cons(active(s(mark(X83))), X2)) [2] mark(c_cons(c_add(X1132, X2132), X2)) -> active(cons(active(add(mark(X1132), mark(X2132))), X2)) [2] mark(c_cons(c_fib(X84), X2)) -> active(cons(active(fib(mark(X84))), X2)) [2] mark(c_cons(c_sel(X1133, X2133), X2)) -> active(cons(active(sel(mark(X1133), mark(X2133))), X2)) [2] mark(c_cons(c_cons(X1134, X2134), X2)) -> active(cons(active(cons(mark(X1134), X2134)), X2)) [2] mark(c_cons(X1, X2)) -> active(cons(c_mark(X1), X2)) [1] mark(c_cons(X1, X2)) -> active(cons(0, X2)) [1] sel(X1, c_active(X2)) -> sel(X1, X2) [1] sel(X1, c_mark(X2)) -> sel(X1, X2) [1] active(c_sel(c_s(c_active(X1135)), c_cons(X, XS))) -> mark(sel(X1135, XS)) [2] active(c_sel(c_s(c_mark(X1136)), c_cons(X, XS))) -> mark(sel(X1136, XS)) [2] active(c_sel(c_s(N), c_cons(X, c_active(X2135)))) -> mark(sel(N, X2135)) [2] active(c_sel(c_s(N), c_cons(X, c_mark(X2136)))) -> mark(sel(N, X2136)) [2] active(c_sel(c_s(N), c_cons(X, XS))) -> mark(c_sel(N, XS)) [1] active(c_sel(c_s(N), c_cons(X, XS))) -> mark(0) [1] encArg(0) -> 0 [0] encArg(cons_active(0)) -> active(0) [0] encArg(cons_active(cons_active(x_1'))) -> active(active(encArg(x_1'))) [0] encArg(cons_active(cons_mark(x_1''))) -> active(mark(encArg(x_1''))) [0] encArg(cons_active(cons_fib(x_11))) -> active(fib(encArg(x_11))) [0] encArg(cons_active(cons_sel(x_12, x_2'))) -> active(sel(encArg(x_12), encArg(x_2'))) [0] encArg(cons_active(cons_fib1(x_13, x_2''))) -> active(fib1(encArg(x_13), encArg(x_2''))) [0] encArg(cons_active(cons_s(x_14))) -> active(s(encArg(x_14))) [0] encArg(cons_active(cons_cons(x_15, x_21))) -> active(cons(encArg(x_15), encArg(x_21))) [0] encArg(cons_active(cons_add(x_16, x_22))) -> active(add(encArg(x_16), encArg(x_22))) [0] encArg(cons_active(x_1)) -> active(0) [0] encArg(cons_mark(0)) -> mark(0) [0] encArg(cons_mark(cons_active(x_17))) -> mark(active(encArg(x_17))) [0] encArg(cons_mark(cons_mark(x_18))) -> mark(mark(encArg(x_18))) [0] encArg(cons_mark(cons_fib(x_19))) -> mark(fib(encArg(x_19))) [0] encArg(cons_mark(cons_sel(x_110, x_23))) -> mark(sel(encArg(x_110), encArg(x_23))) [0] encArg(cons_mark(cons_fib1(x_111, x_24))) -> mark(fib1(encArg(x_111), encArg(x_24))) [0] encArg(cons_mark(cons_s(x_112))) -> mark(s(encArg(x_112))) [0] encArg(cons_mark(cons_cons(x_113, x_25))) -> mark(cons(encArg(x_113), encArg(x_25))) [0] encArg(cons_mark(cons_add(x_114, x_26))) -> mark(add(encArg(x_114), encArg(x_26))) [0] encArg(cons_mark(x_1)) -> mark(0) [0] encArg(cons_fib(0)) -> fib(0) [0] encArg(cons_fib(cons_active(x_115))) -> fib(active(encArg(x_115))) [0] encArg(cons_fib(cons_mark(x_116))) -> fib(mark(encArg(x_116))) [0] encArg(cons_fib(cons_fib(x_117))) -> fib(fib(encArg(x_117))) [0] encArg(cons_fib(cons_sel(x_118, x_27))) -> fib(sel(encArg(x_118), encArg(x_27))) [0] encArg(cons_fib(cons_fib1(x_119, x_28))) -> fib(fib1(encArg(x_119), encArg(x_28))) [0] encArg(cons_fib(cons_s(x_120))) -> fib(s(encArg(x_120))) [0] encArg(cons_fib(cons_cons(x_121, x_29))) -> fib(cons(encArg(x_121), encArg(x_29))) [0] encArg(cons_fib(cons_add(x_122, x_210))) -> fib(add(encArg(x_122), encArg(x_210))) [0] encArg(cons_fib(x_1)) -> fib(0) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(0)) -> s(0) [0] encArg(cons_s(cons_active(x_1199))) -> s(active(encArg(x_1199))) [0] encArg(cons_s(cons_mark(x_1200))) -> s(mark(encArg(x_1200))) [0] encArg(cons_s(cons_fib(x_1201))) -> s(fib(encArg(x_1201))) [0] encArg(cons_s(cons_sel(x_1202, x_299))) -> s(sel(encArg(x_1202), encArg(x_299))) [0] encArg(cons_s(cons_fib1(x_1203, x_2100))) -> s(fib1(encArg(x_1203), encArg(x_2100))) [0] encArg(cons_s(cons_s(x_1204))) -> s(s(encArg(x_1204))) [0] encArg(cons_s(cons_cons(x_1205, x_2101))) -> s(cons(encArg(x_1205), encArg(x_2101))) [0] encArg(cons_s(cons_add(x_1206, x_2102))) -> s(add(encArg(x_1206), encArg(x_2102))) [0] encArg(cons_s(x_1)) -> s(0) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) [0] encode_active(0) -> active(0) [0] encode_active(cons_active(x_1383)) -> active(active(encArg(x_1383))) [0] encode_active(cons_mark(x_1384)) -> active(mark(encArg(x_1384))) [0] encode_active(cons_fib(x_1385)) -> active(fib(encArg(x_1385))) [0] encode_active(cons_sel(x_1386, x_2191)) -> active(sel(encArg(x_1386), encArg(x_2191))) [0] encode_active(cons_fib1(x_1387, x_2192)) -> active(fib1(encArg(x_1387), encArg(x_2192))) [0] encode_active(cons_s(x_1388)) -> active(s(encArg(x_1388))) [0] encode_active(cons_cons(x_1389, x_2193)) -> active(cons(encArg(x_1389), encArg(x_2193))) [0] encode_active(cons_add(x_1390, x_2194)) -> active(add(encArg(x_1390), encArg(x_2194))) [0] encode_active(x_1) -> active(0) [0] encode_fib(0) -> fib(0) [0] encode_fib(cons_active(x_1391)) -> fib(active(encArg(x_1391))) [0] encode_fib(cons_mark(x_1392)) -> fib(mark(encArg(x_1392))) [0] encode_fib(cons_fib(x_1393)) -> fib(fib(encArg(x_1393))) [0] encode_fib(cons_sel(x_1394, x_2195)) -> fib(sel(encArg(x_1394), encArg(x_2195))) [0] encode_fib(cons_fib1(x_1395, x_2196)) -> fib(fib1(encArg(x_1395), encArg(x_2196))) [0] encode_fib(cons_s(x_1396)) -> fib(s(encArg(x_1396))) [0] encode_fib(cons_cons(x_1397, x_2197)) -> fib(cons(encArg(x_1397), encArg(x_2197))) [0] encode_fib(cons_add(x_1398, x_2198)) -> fib(add(encArg(x_1398), encArg(x_2198))) [0] encode_fib(x_1) -> fib(0) [0] encode_mark(0) -> mark(0) [0] encode_mark(cons_active(x_1399)) -> mark(active(encArg(x_1399))) [0] encode_mark(cons_mark(x_1400)) -> mark(mark(encArg(x_1400))) [0] encode_mark(cons_fib(x_1401)) -> mark(fib(encArg(x_1401))) [0] encode_mark(cons_sel(x_1402, x_2199)) -> mark(sel(encArg(x_1402), encArg(x_2199))) [0] encode_mark(cons_fib1(x_1403, x_2200)) -> mark(fib1(encArg(x_1403), encArg(x_2200))) [0] encode_mark(cons_s(x_1404)) -> mark(s(encArg(x_1404))) [0] encode_mark(cons_cons(x_1405, x_2201)) -> mark(cons(encArg(x_1405), encArg(x_2201))) [0] encode_mark(cons_add(x_1406, x_2202)) -> mark(add(encArg(x_1406), encArg(x_2202))) [0] encode_mark(x_1) -> mark(0) [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) [0] encode_s(0) -> s(0) [0] encode_s(cons_active(x_1583)) -> s(active(encArg(x_1583))) [0] encode_s(cons_mark(x_1584)) -> s(mark(encArg(x_1584))) [0] encode_s(cons_fib(x_1585)) -> s(fib(encArg(x_1585))) [0] encode_s(cons_sel(x_1586, x_2291)) -> s(sel(encArg(x_1586), encArg(x_2291))) [0] encode_s(cons_fib1(x_1587, x_2292)) -> s(fib1(encArg(x_1587), encArg(x_2292))) [0] encode_s(cons_s(x_1588)) -> s(s(encArg(x_1588))) [0] encode_s(cons_cons(x_1589, x_2293)) -> s(cons(encArg(x_1589), encArg(x_2293))) [0] encode_s(cons_add(x_1590, x_2294)) -> s(add(encArg(x_1590), encArg(x_2294))) [0] encode_s(x_1) -> s(0) [0] encode_0 -> 0 [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] fib1(x0, x1) -> c_fib1(x0, x1) [0] fib(x0) -> c_fib(x0) [0] add(x0, x1) -> c_add(x0, x1) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> 0 [0] encode_active(v0) -> 0 [0] encode_fib(v0) -> 0 [0] encode_mark(v0) -> 0 [0] encode_sel(v0, v1) -> 0 [0] encode_fib1(v0, v1) -> 0 [0] encode_s(v0) -> 0 [0] encode_0 -> 0 [0] encode_cons(v0, v1) -> 0 [0] encode_add(v0, v1) -> 0 [0] s(v0) -> 0 [0] active(v0) -> 0 [0] fib1(v0, v1) -> 0 [0] fib(v0) -> 0 [0] add(v0, v1) -> 0 [0] cons(v0, v1) -> 0 [0] sel(v0, v1) -> 0 [0] mark(v0) -> 0 [0] The TRS has the following type information: mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add 0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add c_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encArg :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add cons_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add encode_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add Rewrite Strategy: INNERMOST ---------------------------------------- (27) 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 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: active(z) -{ 1 }-> mark(X) :|: X >= 0, XS >= 0, z = 1 + 0 + (1 + X + XS) active(z) -{ 1 }-> mark(X) :|: z = 1 + 0 + X, X >= 0 active(z) -{ 2 }-> mark(sel(N, X2135)) :|: z = 1 + (1 + N) + (1 + X + (1 + X2135)), X >= 0, N >= 0, X2135 >= 0 active(z) -{ 2 }-> mark(sel(N, X2136)) :|: X >= 0, X2136 >= 0, z = 1 + (1 + N) + (1 + X + (1 + X2136)), N >= 0 active(z) -{ 1 }-> mark(sel(N, fib1(0, 0))) :|: z = 1 + N, N >= 0 active(z) -{ 1 }-> mark(sel(N, fib1(0, 1 + 0))) :|: z = 1 + N, N >= 0 active(z) -{ 1 }-> mark(sel(N, fib1(1 + 0, 0))) :|: z = 1 + N, N >= 0 active(z) -{ 1 }-> mark(sel(N, fib1(1 + 0, 1 + 0))) :|: z = 1 + N, N >= 0 active(z) -{ 2 }-> mark(sel(X1135, XS)) :|: X1135 >= 0, z = 1 + (1 + (1 + X1135)) + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 2 }-> mark(sel(X1136, XS)) :|: z = 1 + (1 + (1 + X1136)) + (1 + X + XS), X1136 >= 0, X >= 0, XS >= 0 active(z) -{ 2 }-> mark(s(add(X, X289))) :|: z = 1 + (1 + X) + (1 + X289), X >= 0, X289 >= 0 active(z) -{ 2 }-> mark(s(add(X, X290))) :|: z = 1 + (1 + X) + (1 + X290), X >= 0, X290 >= 0 active(z) -{ 2 }-> mark(s(add(X189, Y))) :|: Y >= 0, X189 >= 0, z = 1 + (1 + (1 + X189)) + Y active(z) -{ 2 }-> mark(s(add(X190, Y))) :|: z = 1 + (1 + (1 + X190)) + Y, Y >= 0, X190 >= 0 active(z) -{ 1 }-> mark(s(0)) :|: z = 1 + (1 + X) + Y, Y >= 0, X >= 0 active(z) -{ 1 }-> mark(s(1 + X + Y)) :|: z = 1 + (1 + X) + Y, Y >= 0, X >= 0 active(z) -{ 1 }-> mark(cons(X, fib1(Y, 0))) :|: Y >= 0, z = 1 + X + Y, X >= 0 active(z) -{ 1 }-> mark(cons(X, fib1(Y, 1 + X + Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 active(z) -{ 2 }-> mark(cons(X, fib1(1 + X287, add(X, X287)))) :|: z = 1 + X + (1 + X287), X >= 0, X287 >= 0 active(z) -{ 2 }-> mark(cons(X, fib1(1 + X288, add(X, X288)))) :|: X >= 0, X288 >= 0, z = 1 + X + (1 + X288) active(z) -{ 2 }-> mark(cons(1 + X187, fib1(Y, add(X187, Y)))) :|: X187 >= 0, Y >= 0, z = 1 + (1 + X187) + Y active(z) -{ 2 }-> mark(cons(1 + X188, fib1(Y, add(X188, Y)))) :|: Y >= 0, z = 1 + (1 + X188) + Y, X188 >= 0 active(z) -{ 1 }-> mark(0) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(1 + N + XS) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 active(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 add(z, z') -{ 1 }-> add(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 add(z, z') -{ 1 }-> add(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 add(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 cons(z, z') -{ 1 }-> cons(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 cons(z, z') -{ 1 }-> cons(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cons(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> sel(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> s(sel(encArg(x_1202), encArg(x_299))) :|: z = 1 + (1 + x_1202 + x_299), x_299 >= 0, x_1202 >= 0 encArg(z) -{ 0 }-> s(s(encArg(x_1204))) :|: x_1204 >= 0, z = 1 + (1 + x_1204) encArg(z) -{ 0 }-> s(mark(encArg(x_1200))) :|: x_1200 >= 0, z = 1 + (1 + x_1200) encArg(z) -{ 0 }-> s(fib1(encArg(x_1203), encArg(x_2100))) :|: x_2100 >= 0, z = 1 + (1 + x_1203 + x_2100), x_1203 >= 0 encArg(z) -{ 0 }-> s(fib(encArg(x_1201))) :|: x_1201 >= 0, z = 1 + (1 + x_1201) encArg(z) -{ 0 }-> s(cons(encArg(x_1205), encArg(x_2101))) :|: z = 1 + (1 + x_1205 + x_2101), x_1205 >= 0, x_2101 >= 0 encArg(z) -{ 0 }-> s(add(encArg(x_1206), encArg(x_2102))) :|: x_1206 >= 0, x_2102 >= 0, z = 1 + (1 + x_1206 + x_2102) encArg(z) -{ 0 }-> s(active(encArg(x_1199))) :|: z = 1 + (1 + x_1199), x_1199 >= 0 encArg(z) -{ 0 }-> s(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> s(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> mark(sel(encArg(x_110), encArg(x_23))) :|: x_23 >= 0, x_110 >= 0, z = 1 + (1 + x_110 + x_23) encArg(z) -{ 0 }-> mark(s(encArg(x_112))) :|: x_112 >= 0, z = 1 + (1 + x_112) encArg(z) -{ 0 }-> mark(mark(encArg(x_18))) :|: z = 1 + (1 + x_18), x_18 >= 0 encArg(z) -{ 0 }-> mark(fib1(encArg(x_111), encArg(x_24))) :|: z = 1 + (1 + x_111 + x_24), x_24 >= 0, x_111 >= 0 encArg(z) -{ 0 }-> mark(fib(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0 encArg(z) -{ 0 }-> mark(cons(encArg(x_113), encArg(x_25))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_25), x_25 >= 0 encArg(z) -{ 0 }-> mark(add(encArg(x_114), encArg(x_26))) :|: z = 1 + (1 + x_114 + x_26), x_114 >= 0, x_26 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(x_17))) :|: x_17 >= 0, z = 1 + (1 + x_17) encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> fib1(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> fib(sel(encArg(x_118), encArg(x_27))) :|: z = 1 + (1 + x_118 + x_27), x_27 >= 0, x_118 >= 0 encArg(z) -{ 0 }-> fib(s(encArg(x_120))) :|: x_120 >= 0, z = 1 + (1 + x_120) encArg(z) -{ 0 }-> fib(mark(encArg(x_116))) :|: z = 1 + (1 + x_116), x_116 >= 0 encArg(z) -{ 0 }-> fib(fib1(encArg(x_119), encArg(x_28))) :|: z = 1 + (1 + x_119 + x_28), x_28 >= 0, x_119 >= 0 encArg(z) -{ 0 }-> fib(fib(encArg(x_117))) :|: z = 1 + (1 + x_117), x_117 >= 0 encArg(z) -{ 0 }-> fib(cons(encArg(x_121), encArg(x_29))) :|: z = 1 + (1 + x_121 + x_29), x_121 >= 0, x_29 >= 0 encArg(z) -{ 0 }-> fib(add(encArg(x_122), encArg(x_210))) :|: x_122 >= 0, z = 1 + (1 + x_122 + x_210), x_210 >= 0 encArg(z) -{ 0 }-> fib(active(encArg(x_115))) :|: z = 1 + (1 + x_115), x_115 >= 0 encArg(z) -{ 0 }-> fib(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> fib(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> cons(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> add(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> active(sel(encArg(x_12), encArg(x_2'))) :|: z = 1 + (1 + x_12 + x_2'), x_2' >= 0, x_12 >= 0 encArg(z) -{ 0 }-> active(s(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14) encArg(z) -{ 0 }-> active(mark(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> active(fib1(encArg(x_13), encArg(x_2''))) :|: x_13 >= 0, x_2'' >= 0, z = 1 + (1 + x_13 + x_2'') encArg(z) -{ 0 }-> active(fib(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11) encArg(z) -{ 0 }-> active(cons(encArg(x_15), encArg(x_21))) :|: x_15 >= 0, z = 1 + (1 + x_15 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(add(encArg(x_16), encArg(x_22))) :|: x_16 >= 0, x_22 >= 0, z = 1 + (1 + x_16 + x_22) encArg(z) -{ 0 }-> active(active(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> active(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> active(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_active(z) -{ 0 }-> active(sel(encArg(x_1386), encArg(x_2191))) :|: x_2191 >= 0, x_1386 >= 0, z = 1 + x_1386 + x_2191 encode_active(z) -{ 0 }-> active(s(encArg(x_1388))) :|: z = 1 + x_1388, x_1388 >= 0 encode_active(z) -{ 0 }-> active(mark(encArg(x_1384))) :|: z = 1 + x_1384, x_1384 >= 0 encode_active(z) -{ 0 }-> active(fib1(encArg(x_1387), encArg(x_2192))) :|: z = 1 + x_1387 + x_2192, x_1387 >= 0, x_2192 >= 0 encode_active(z) -{ 0 }-> active(fib(encArg(x_1385))) :|: z = 1 + x_1385, x_1385 >= 0 encode_active(z) -{ 0 }-> active(cons(encArg(x_1389), encArg(x_2193))) :|: z = 1 + x_1389 + x_2193, x_2193 >= 0, x_1389 >= 0 encode_active(z) -{ 0 }-> active(add(encArg(x_1390), encArg(x_2194))) :|: x_1390 >= 0, x_2194 >= 0, z = 1 + x_1390 + x_2194 encode_active(z) -{ 0 }-> active(active(encArg(x_1383))) :|: x_1383 >= 0, z = 1 + x_1383 encode_active(z) -{ 0 }-> active(0) :|: z = 0 encode_active(z) -{ 0 }-> active(0) :|: x_1 >= 0, z = x_1 encode_active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_add(z, z') -{ 0 }-> add(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons(z, z') -{ 0 }-> cons(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_fib(z) -{ 0 }-> fib(sel(encArg(x_1394), encArg(x_2195))) :|: x_1394 >= 0, z = 1 + x_1394 + x_2195, x_2195 >= 0 encode_fib(z) -{ 0 }-> fib(s(encArg(x_1396))) :|: x_1396 >= 0, z = 1 + x_1396 encode_fib(z) -{ 0 }-> fib(mark(encArg(x_1392))) :|: z = 1 + x_1392, x_1392 >= 0 encode_fib(z) -{ 0 }-> fib(fib1(encArg(x_1395), encArg(x_2196))) :|: x_1395 >= 0, z = 1 + x_1395 + x_2196, x_2196 >= 0 encode_fib(z) -{ 0 }-> fib(fib(encArg(x_1393))) :|: x_1393 >= 0, z = 1 + x_1393 encode_fib(z) -{ 0 }-> fib(cons(encArg(x_1397), encArg(x_2197))) :|: x_1397 >= 0, z = 1 + x_1397 + x_2197, x_2197 >= 0 encode_fib(z) -{ 0 }-> fib(add(encArg(x_1398), encArg(x_2198))) :|: x_2198 >= 0, z = 1 + x_1398 + x_2198, x_1398 >= 0 encode_fib(z) -{ 0 }-> fib(active(encArg(x_1391))) :|: z = 1 + x_1391, x_1391 >= 0 encode_fib(z) -{ 0 }-> fib(0) :|: z = 0 encode_fib(z) -{ 0 }-> fib(0) :|: x_1 >= 0, z = x_1 encode_fib(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_fib1(z, z') -{ 0 }-> fib1(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_mark(z) -{ 0 }-> mark(sel(encArg(x_1402), encArg(x_2199))) :|: x_1402 >= 0, x_2199 >= 0, z = 1 + x_1402 + x_2199 encode_mark(z) -{ 0 }-> mark(s(encArg(x_1404))) :|: x_1404 >= 0, z = 1 + x_1404 encode_mark(z) -{ 0 }-> mark(mark(encArg(x_1400))) :|: z = 1 + x_1400, x_1400 >= 0 encode_mark(z) -{ 0 }-> mark(fib1(encArg(x_1403), encArg(x_2200))) :|: z = 1 + x_1403 + x_2200, x_1403 >= 0, x_2200 >= 0 encode_mark(z) -{ 0 }-> mark(fib(encArg(x_1401))) :|: z = 1 + x_1401, x_1401 >= 0 encode_mark(z) -{ 0 }-> mark(cons(encArg(x_1405), encArg(x_2201))) :|: x_1405 >= 0, x_2201 >= 0, z = 1 + x_1405 + x_2201 encode_mark(z) -{ 0 }-> mark(add(encArg(x_1406), encArg(x_2202))) :|: z = 1 + x_1406 + x_2202, x_1406 >= 0, x_2202 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(x_1399))) :|: z = 1 + x_1399, x_1399 >= 0 encode_mark(z) -{ 0 }-> mark(0) :|: z = 0 encode_mark(z) -{ 0 }-> mark(0) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> s(sel(encArg(x_1586), encArg(x_2291))) :|: z = 1 + x_1586 + x_2291, x_2291 >= 0, x_1586 >= 0 encode_s(z) -{ 0 }-> s(s(encArg(x_1588))) :|: z = 1 + x_1588, x_1588 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(x_1584))) :|: x_1584 >= 0, z = 1 + x_1584 encode_s(z) -{ 0 }-> s(fib1(encArg(x_1587), encArg(x_2292))) :|: x_2292 >= 0, z = 1 + x_1587 + x_2292, x_1587 >= 0 encode_s(z) -{ 0 }-> s(fib(encArg(x_1585))) :|: x_1585 >= 0, z = 1 + x_1585 encode_s(z) -{ 0 }-> s(cons(encArg(x_1589), encArg(x_2293))) :|: x_1589 >= 0, x_2293 >= 0, z = 1 + x_1589 + x_2293 encode_s(z) -{ 0 }-> s(add(encArg(x_1590), encArg(x_2294))) :|: x_1590 >= 0, z = 1 + x_1590 + x_2294, x_2294 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(x_1583))) :|: z = 1 + x_1583, x_1583 >= 0 encode_s(z) -{ 0 }-> s(0) :|: z = 0 encode_s(z) -{ 0 }-> s(0) :|: x_1 >= 0, z = x_1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_sel(z, z') -{ 0 }-> sel(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib(z) -{ 1 }-> fib(X) :|: z = 1 + X, X >= 0 fib(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 fib(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 fib1(z, z') -{ 1 }-> fib1(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 fib1(z, z') -{ 1 }-> fib1(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib1(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 mark(z) -{ 1 }-> active(sel(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(s(active(sel(mark(X141), mark(X241))))) :|: z = 1 + (1 + X141 + X241), X241 >= 0, X141 >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(X39))))) :|: z = 1 + (1 + X39), X39 >= 0 mark(z) -{ 2 }-> active(s(active(fib1(mark(X139), mark(X239))))) :|: z = 1 + (1 + X139 + X239), X239 >= 0, X139 >= 0 mark(z) -{ 2 }-> active(s(active(fib(mark(X40))))) :|: z = 1 + (1 + X40), X40 >= 0 mark(z) -{ 2 }-> active(s(active(cons(mark(X142), X242)))) :|: z = 1 + (1 + X142 + X242), X242 >= 0, X142 >= 0 mark(z) -{ 2 }-> active(s(active(add(mark(X140), mark(X240))))) :|: z = 1 + (1 + X140 + X240), X240 >= 0, X140 >= 0 mark(z) -{ 2 }-> active(s(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(s(0)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(s(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(fib1(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(fib(active(sel(mark(X185), mark(X285))))) :|: X285 >= 0, X185 >= 0, z = 1 + (1 + X185 + X285) mark(z) -{ 2 }-> active(fib(active(s(mark(X61))))) :|: X61 >= 0, z = 1 + (1 + X61) mark(z) -{ 2 }-> active(fib(active(fib1(mark(X183), mark(X283))))) :|: X183 >= 0, X283 >= 0, z = 1 + (1 + X183 + X283) mark(z) -{ 2 }-> active(fib(active(fib(mark(X62))))) :|: X62 >= 0, z = 1 + (1 + X62) mark(z) -{ 2 }-> active(fib(active(cons(mark(X186), X286)))) :|: X286 >= 0, X186 >= 0, z = 1 + (1 + X186 + X286) mark(z) -{ 2 }-> active(fib(active(add(mark(X184), mark(X284))))) :|: z = 1 + (1 + X184 + X284), X184 >= 0, X284 >= 0 mark(z) -{ 2 }-> active(fib(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(fib(0)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(fib(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> active(cons(active(sel(mark(X1133), mark(X2133))), X2)) :|: X2133 >= 0, z = 1 + (1 + X1133 + X2133) + X2, X2 >= 0, X1133 >= 0 mark(z) -{ 2 }-> active(cons(active(s(mark(X83))), X2)) :|: z = 1 + (1 + X83) + X2, X83 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(fib1(mark(X1131), mark(X2131))), X2)) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> active(cons(active(fib(mark(X84))), X2)) :|: z = 1 + (1 + X84) + X2, X84 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(cons(mark(X1134), X2134)), X2)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134) + X2, X1134 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(add(mark(X1132), mark(X2132))), X2)) :|: X2132 >= 0, z = 1 + (1 + X1132 + X2132) + X2, X2 >= 0, X1132 >= 0 mark(z) -{ 2 }-> active(cons(active(0), X2)) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 1 }-> active(cons(0, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(cons(1 + X1, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(add(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(0) :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 s(z) -{ 1 }-> s(X) :|: z = 1 + X, X >= 0 s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 sel(z, z') -{ 1 }-> sel(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 sel(z, z') -{ 1 }-> sel(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 sel(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: active(z) -{ 1 }-> mark(X) :|: X >= 0, XS >= 0, z = 1 + 0 + (1 + X + XS) active(z) -{ 2 }-> mark(sel(N, X2135)) :|: z = 1 + (1 + N) + (1 + X + (1 + X2135)), X >= 0, N >= 0, X2135 >= 0 active(z) -{ 2 }-> mark(sel(N, X2136)) :|: X >= 0, X2136 >= 0, z = 1 + (1 + N) + (1 + X + (1 + X2136)), N >= 0 active(z) -{ 2 }-> mark(sel(X1135, XS)) :|: X1135 >= 0, z = 1 + (1 + (1 + X1135)) + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 2 }-> mark(sel(X1136, XS)) :|: z = 1 + (1 + (1 + X1136)) + (1 + X + XS), X1136 >= 0, X >= 0, XS >= 0 active(z) -{ 1 }-> mark(sel(z - 1, fib1(0, 0))) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(sel(z - 1, fib1(0, 1 + 0))) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(sel(z - 1, fib1(1 + 0, 0))) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(sel(z - 1, fib1(1 + 0, 1 + 0))) :|: z - 1 >= 0 active(z) -{ 2 }-> mark(s(add(X, X289))) :|: z = 1 + (1 + X) + (1 + X289), X >= 0, X289 >= 0 active(z) -{ 2 }-> mark(s(add(X, X290))) :|: z = 1 + (1 + X) + (1 + X290), X >= 0, X290 >= 0 active(z) -{ 2 }-> mark(s(add(X189, Y))) :|: Y >= 0, X189 >= 0, z = 1 + (1 + (1 + X189)) + Y active(z) -{ 2 }-> mark(s(add(X190, Y))) :|: z = 1 + (1 + (1 + X190)) + Y, Y >= 0, X190 >= 0 active(z) -{ 1 }-> mark(s(0)) :|: z = 1 + (1 + X) + Y, Y >= 0, X >= 0 active(z) -{ 1 }-> mark(s(1 + X + Y)) :|: z = 1 + (1 + X) + Y, Y >= 0, X >= 0 active(z) -{ 1 }-> mark(cons(X, fib1(Y, 0))) :|: Y >= 0, z = 1 + X + Y, X >= 0 active(z) -{ 1 }-> mark(cons(X, fib1(Y, 1 + X + Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 active(z) -{ 2 }-> mark(cons(X, fib1(1 + X287, add(X, X287)))) :|: z = 1 + X + (1 + X287), X >= 0, X287 >= 0 active(z) -{ 2 }-> mark(cons(X, fib1(1 + X288, add(X, X288)))) :|: X >= 0, X288 >= 0, z = 1 + X + (1 + X288) active(z) -{ 2 }-> mark(cons(1 + X187, fib1(Y, add(X187, Y)))) :|: X187 >= 0, Y >= 0, z = 1 + (1 + X187) + Y active(z) -{ 2 }-> mark(cons(1 + X188, fib1(Y, add(X188, Y)))) :|: Y >= 0, z = 1 + (1 + X188) + Y, X188 >= 0 active(z) -{ 1 }-> mark(0) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(z - 1) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(1 + N + XS) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 0 }-> 0 :|: z >= 0 active(z) -{ 0 }-> 1 + z :|: z >= 0 add(z, z') -{ 1 }-> add(z, z' - 1) :|: z >= 0, z' - 1 >= 0 add(z, z') -{ 1 }-> add(z - 1, z') :|: z - 1 >= 0, z' >= 0 add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 add(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 cons(z, z') -{ 1 }-> cons(z, z' - 1) :|: z >= 0, z' - 1 >= 0 cons(z, z') -{ 1 }-> cons(z - 1, z') :|: z - 1 >= 0, z' >= 0 cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 cons(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 encArg(z) -{ 0 }-> sel(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> s(sel(encArg(x_1202), encArg(x_299))) :|: z = 1 + (1 + x_1202 + x_299), x_299 >= 0, x_1202 >= 0 encArg(z) -{ 0 }-> s(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(fib1(encArg(x_1203), encArg(x_2100))) :|: x_2100 >= 0, z = 1 + (1 + x_1203 + x_2100), x_1203 >= 0 encArg(z) -{ 0 }-> s(fib(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(cons(encArg(x_1205), encArg(x_2101))) :|: z = 1 + (1 + x_1205 + x_2101), x_1205 >= 0, x_2101 >= 0 encArg(z) -{ 0 }-> s(add(encArg(x_1206), encArg(x_2102))) :|: x_1206 >= 0, x_2102 >= 0, z = 1 + (1 + x_1206 + x_2102) encArg(z) -{ 0 }-> s(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> s(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> mark(sel(encArg(x_110), encArg(x_23))) :|: x_23 >= 0, x_110 >= 0, z = 1 + (1 + x_110 + x_23) encArg(z) -{ 0 }-> mark(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(fib1(encArg(x_111), encArg(x_24))) :|: z = 1 + (1 + x_111 + x_24), x_24 >= 0, x_111 >= 0 encArg(z) -{ 0 }-> mark(fib(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(cons(encArg(x_113), encArg(x_25))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_25), x_25 >= 0 encArg(z) -{ 0 }-> mark(add(encArg(x_114), encArg(x_26))) :|: z = 1 + (1 + x_114 + x_26), x_114 >= 0, x_26 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> fib1(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> fib(sel(encArg(x_118), encArg(x_27))) :|: z = 1 + (1 + x_118 + x_27), x_27 >= 0, x_118 >= 0 encArg(z) -{ 0 }-> fib(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> fib(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> fib(fib1(encArg(x_119), encArg(x_28))) :|: z = 1 + (1 + x_119 + x_28), x_28 >= 0, x_119 >= 0 encArg(z) -{ 0 }-> fib(fib(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> fib(cons(encArg(x_121), encArg(x_29))) :|: z = 1 + (1 + x_121 + x_29), x_121 >= 0, x_29 >= 0 encArg(z) -{ 0 }-> fib(add(encArg(x_122), encArg(x_210))) :|: x_122 >= 0, z = 1 + (1 + x_122 + x_210), x_210 >= 0 encArg(z) -{ 0 }-> fib(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> fib(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> fib(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> cons(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> add(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> active(sel(encArg(x_12), encArg(x_2'))) :|: z = 1 + (1 + x_12 + x_2'), x_2' >= 0, x_12 >= 0 encArg(z) -{ 0 }-> active(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(fib1(encArg(x_13), encArg(x_2''))) :|: x_13 >= 0, x_2'' >= 0, z = 1 + (1 + x_13 + x_2'') encArg(z) -{ 0 }-> active(fib(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(cons(encArg(x_15), encArg(x_21))) :|: x_15 >= 0, z = 1 + (1 + x_15 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(add(encArg(x_16), encArg(x_22))) :|: x_16 >= 0, x_22 >= 0, z = 1 + (1 + x_16 + x_22) encArg(z) -{ 0 }-> active(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> active(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_0 -{ 0 }-> 0 :|: encode_active(z) -{ 0 }-> active(sel(encArg(x_1386), encArg(x_2191))) :|: x_2191 >= 0, x_1386 >= 0, z = 1 + x_1386 + x_2191 encode_active(z) -{ 0 }-> active(s(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(fib1(encArg(x_1387), encArg(x_2192))) :|: z = 1 + x_1387 + x_2192, x_1387 >= 0, x_2192 >= 0 encode_active(z) -{ 0 }-> active(fib(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(cons(encArg(x_1389), encArg(x_2193))) :|: z = 1 + x_1389 + x_2193, x_2193 >= 0, x_1389 >= 0 encode_active(z) -{ 0 }-> active(add(encArg(x_1390), encArg(x_2194))) :|: x_1390 >= 0, x_2194 >= 0, z = 1 + x_1390 + x_2194 encode_active(z) -{ 0 }-> active(active(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(0) :|: z = 0 encode_active(z) -{ 0 }-> active(0) :|: z >= 0 encode_active(z) -{ 0 }-> 0 :|: z >= 0 encode_add(z, z') -{ 0 }-> add(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_cons(z, z') -{ 0 }-> cons(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_fib(z) -{ 0 }-> fib(sel(encArg(x_1394), encArg(x_2195))) :|: x_1394 >= 0, z = 1 + x_1394 + x_2195, x_2195 >= 0 encode_fib(z) -{ 0 }-> fib(s(encArg(z - 1))) :|: z - 1 >= 0 encode_fib(z) -{ 0 }-> fib(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_fib(z) -{ 0 }-> fib(fib1(encArg(x_1395), encArg(x_2196))) :|: x_1395 >= 0, z = 1 + x_1395 + x_2196, x_2196 >= 0 encode_fib(z) -{ 0 }-> fib(fib(encArg(z - 1))) :|: z - 1 >= 0 encode_fib(z) -{ 0 }-> fib(cons(encArg(x_1397), encArg(x_2197))) :|: x_1397 >= 0, z = 1 + x_1397 + x_2197, x_2197 >= 0 encode_fib(z) -{ 0 }-> fib(add(encArg(x_1398), encArg(x_2198))) :|: x_2198 >= 0, z = 1 + x_1398 + x_2198, x_1398 >= 0 encode_fib(z) -{ 0 }-> fib(active(encArg(z - 1))) :|: z - 1 >= 0 encode_fib(z) -{ 0 }-> fib(0) :|: z = 0 encode_fib(z) -{ 0 }-> fib(0) :|: z >= 0 encode_fib(z) -{ 0 }-> 0 :|: z >= 0 encode_fib1(z, z') -{ 0 }-> fib1(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_mark(z) -{ 0 }-> mark(sel(encArg(x_1402), encArg(x_2199))) :|: x_1402 >= 0, x_2199 >= 0, z = 1 + x_1402 + x_2199 encode_mark(z) -{ 0 }-> mark(s(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(fib1(encArg(x_1403), encArg(x_2200))) :|: z = 1 + x_1403 + x_2200, x_1403 >= 0, x_2200 >= 0 encode_mark(z) -{ 0 }-> mark(fib(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(cons(encArg(x_1405), encArg(x_2201))) :|: x_1405 >= 0, x_2201 >= 0, z = 1 + x_1405 + x_2201 encode_mark(z) -{ 0 }-> mark(add(encArg(x_1406), encArg(x_2202))) :|: z = 1 + x_1406 + x_2202, x_1406 >= 0, x_2202 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(0) :|: z = 0 encode_mark(z) -{ 0 }-> mark(0) :|: z >= 0 encode_mark(z) -{ 0 }-> 0 :|: z >= 0 encode_s(z) -{ 0 }-> s(sel(encArg(x_1586), encArg(x_2291))) :|: z = 1 + x_1586 + x_2291, x_2291 >= 0, x_1586 >= 0 encode_s(z) -{ 0 }-> s(s(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(fib1(encArg(x_1587), encArg(x_2292))) :|: x_2292 >= 0, z = 1 + x_1587 + x_2292, x_1587 >= 0 encode_s(z) -{ 0 }-> s(fib(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(cons(encArg(x_1589), encArg(x_2293))) :|: x_1589 >= 0, x_2293 >= 0, z = 1 + x_1589 + x_2293 encode_s(z) -{ 0 }-> s(add(encArg(x_1590), encArg(x_2294))) :|: x_1590 >= 0, z = 1 + x_1590 + x_2294, x_2294 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(0) :|: z = 0 encode_s(z) -{ 0 }-> s(0) :|: z >= 0 encode_s(z) -{ 0 }-> 0 :|: z >= 0 encode_sel(z, z') -{ 0 }-> sel(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_sel(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib(z) -{ 1 }-> fib(z - 1) :|: z - 1 >= 0 fib(z) -{ 0 }-> 0 :|: z >= 0 fib(z) -{ 0 }-> 1 + z :|: z >= 0 fib1(z, z') -{ 1 }-> fib1(z, z' - 1) :|: z >= 0, z' - 1 >= 0 fib1(z, z') -{ 1 }-> fib1(z - 1, z') :|: z - 1 >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 fib1(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> active(sel(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(s(active(sel(mark(X141), mark(X241))))) :|: z = 1 + (1 + X141 + X241), X241 >= 0, X141 >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(fib1(mark(X139), mark(X239))))) :|: z = 1 + (1 + X139 + X239), X239 >= 0, X139 >= 0 mark(z) -{ 2 }-> active(s(active(fib(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(cons(mark(X142), X242)))) :|: z = 1 + (1 + X142 + X242), X242 >= 0, X142 >= 0 mark(z) -{ 2 }-> active(s(active(add(mark(X140), mark(X240))))) :|: z = 1 + (1 + X140 + X240), X240 >= 0, X140 >= 0 mark(z) -{ 2 }-> active(s(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(s(0)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(s(1 + (z - 1))) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(fib1(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(fib(active(sel(mark(X185), mark(X285))))) :|: X285 >= 0, X185 >= 0, z = 1 + (1 + X185 + X285) mark(z) -{ 2 }-> active(fib(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(fib(active(fib1(mark(X183), mark(X283))))) :|: X183 >= 0, X283 >= 0, z = 1 + (1 + X183 + X283) mark(z) -{ 2 }-> active(fib(active(fib(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(fib(active(cons(mark(X186), X286)))) :|: X286 >= 0, X186 >= 0, z = 1 + (1 + X186 + X286) mark(z) -{ 2 }-> active(fib(active(add(mark(X184), mark(X284))))) :|: z = 1 + (1 + X184 + X284), X184 >= 0, X284 >= 0 mark(z) -{ 2 }-> active(fib(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(fib(0)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(fib(1 + (z - 1))) :|: z - 1 >= 0 mark(z) -{ 2 }-> active(cons(active(sel(mark(X1133), mark(X2133))), X2)) :|: X2133 >= 0, z = 1 + (1 + X1133 + X2133) + X2, X2 >= 0, X1133 >= 0 mark(z) -{ 2 }-> active(cons(active(s(mark(X83))), X2)) :|: z = 1 + (1 + X83) + X2, X83 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(fib1(mark(X1131), mark(X2131))), X2)) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> active(cons(active(fib(mark(X84))), X2)) :|: z = 1 + (1 + X84) + X2, X84 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(cons(mark(X1134), X2134)), X2)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134) + X2, X1134 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(add(mark(X1132), mark(X2132))), X2)) :|: X2132 >= 0, z = 1 + (1 + X1132 + X2132) + X2, X2 >= 0, X1132 >= 0 mark(z) -{ 2 }-> active(cons(active(0), z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(cons(0, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(cons(1 + X1, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(add(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(0) :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + z :|: z >= 0 s(z) -{ 1 }-> s(z - 1) :|: z - 1 >= 0 s(z) -{ 0 }-> 0 :|: z >= 0 s(z) -{ 0 }-> 1 + z :|: z >= 0 sel(z, z') -{ 1 }-> sel(z, z' - 1) :|: z >= 0, z' - 1 >= 0 sel(z, z') -{ 1 }-> sel(z - 1, z') :|: z - 1 >= 0, z' >= 0 sel(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 sel(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 ---------------------------------------- (31) 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: encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_fib(v0) -> null_encode_fib [0] encode_mark(v0) -> null_encode_mark [0] encode_sel(v0, v1) -> null_encode_sel [0] encode_fib1(v0, v1) -> null_encode_fib1 [0] encode_s(v0) -> null_encode_s [0] encode_0 -> null_encode_0 [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_add(v0, v1) -> null_encode_add [0] s(v0) -> null_s [0] active(v0) -> null_active [0] fib1(v0, v1) -> null_fib1 [0] fib(v0) -> null_fib [0] add(v0, v1) -> null_add [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_fib, null_encode_mark, null_encode_sel, null_encode_fib1, null_encode_s, null_encode_0, null_encode_cons, null_encode_add, null_s, null_active, null_fib1, null_fib, null_add, null_cons, null_sel, null_mark ---------------------------------------- (32) 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: mark(0) -> active(0) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_fib1(X1, X2)) -> active(fib1(mark(X1), mark(X2))) [1] add(c_active(X1), X2) -> add(X1, X2) [1] fib(c_mark(X)) -> fib(X) [1] fib1(X1, c_mark(X2)) -> fib1(X1, X2) [1] add(X1, c_mark(X2)) -> add(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_add(X1, X2)) -> active(add(mark(X1), mark(X2))) [1] s(c_active(X)) -> s(X) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] mark(c_fib(X)) -> active(fib(mark(X))) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] fib1(c_active(X1), X2) -> fib1(X1, X2) [1] active(c_fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) [1] fib1(X1, c_active(X2)) -> fib1(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] active(c_fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] fib1(c_mark(X1), X2) -> fib1(X1, X2) [1] add(c_mark(X1), X2) -> add(X1, X2) [1] fib(c_active(X)) -> fib(X) [1] add(X1, c_active(X2)) -> add(X1, X2) [1] s(c_mark(X)) -> s(X) [1] active(c_add(c_s(X), Y)) -> mark(s(add(X, Y))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] active(c_add(0, X)) -> mark(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] sel(X1, c_active(X2)) -> sel(X1, X2) [1] sel(X1, c_mark(X2)) -> sel(X1, X2) [1] active(c_sel(c_s(N), c_cons(X, XS))) -> mark(sel(N, XS)) [1] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_fib(x_1)) -> fib(encArg(x_1)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encArg(cons_fib1(x_1, x_2)) -> fib1(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_fib(x_1) -> fib(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] encode_fib1(x_1, x_2) -> fib1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] fib1(x0, x1) -> c_fib1(x0, x1) [0] fib(x0) -> c_fib(x0) [0] add(x0, x1) -> c_add(x0, x1) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_fib(v0) -> null_encode_fib [0] encode_mark(v0) -> null_encode_mark [0] encode_sel(v0, v1) -> null_encode_sel [0] encode_fib1(v0, v1) -> null_encode_fib1 [0] encode_s(v0) -> null_encode_s [0] encode_0 -> null_encode_0 [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_add(v0, v1) -> null_encode_add [0] s(v0) -> null_s [0] active(v0) -> null_active [0] fib1(v0, v1) -> null_fib1 [0] fib(v0) -> null_fib [0] add(v0, v1) -> null_add [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark 0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark c_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encArg :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark cons_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark encode_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark -> 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encArg :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_0 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_encode_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_s :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_active :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_fib1 :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_fib :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_add :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_cons :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_sel :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark null_mark :: 0:c_cons:c_sel:c_fib1:c_active:c_mark:c_s:c_add:c_fib:cons_active:cons_mark:cons_fib:cons_sel:cons_fib1:cons_s:cons_cons:cons_add:null_encArg:null_encode_active:null_encode_fib:null_encode_mark:null_encode_sel:null_encode_fib1:null_encode_s:null_encode_0:null_encode_cons:null_encode_add:null_s:null_active:null_fib1:null_fib:null_add:null_cons:null_sel:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (33) 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_encArg => 0 null_encode_active => 0 null_encode_fib => 0 null_encode_mark => 0 null_encode_sel => 0 null_encode_fib1 => 0 null_encode_s => 0 null_encode_0 => 0 null_encode_cons => 0 null_encode_add => 0 null_s => 0 null_active => 0 null_fib1 => 0 null_fib => 0 null_add => 0 null_cons => 0 null_sel => 0 null_mark => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: active(z) -{ 1 }-> mark(X) :|: X >= 0, XS >= 0, z = 1 + 0 + (1 + X + XS) active(z) -{ 1 }-> mark(X) :|: z = 1 + 0 + X, X >= 0 active(z) -{ 1 }-> mark(sel(N, XS)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(sel(N, fib1(s(0), s(0)))) :|: z = 1 + N, N >= 0 active(z) -{ 1 }-> mark(s(add(X, Y))) :|: z = 1 + (1 + X) + Y, Y >= 0, X >= 0 active(z) -{ 1 }-> mark(cons(X, fib1(Y, add(X, Y)))) :|: Y >= 0, z = 1 + X + Y, X >= 0 active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 active(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 add(z, z') -{ 1 }-> add(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 add(z, z') -{ 1 }-> add(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 add(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 cons(z, z') -{ 1 }-> cons(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 cons(z, z') -{ 1 }-> cons(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cons(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> sel(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> s(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> mark(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> fib1(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> fib(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> cons(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> add(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> active(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_active(z) -{ 0 }-> active(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_add(z, z') -{ 0 }-> add(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons(z, z') -{ 0 }-> cons(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_fib(z) -{ 0 }-> fib(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_fib(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_fib1(z, z') -{ 0 }-> fib1(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_mark(z) -{ 0 }-> mark(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> s(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_sel(z, z') -{ 0 }-> sel(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib(z) -{ 1 }-> fib(X) :|: z = 1 + X, X >= 0 fib(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 fib(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 fib1(z, z') -{ 1 }-> fib1(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 fib1(z, z') -{ 1 }-> fib1(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 fib1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fib1(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 mark(z) -{ 1 }-> active(sel(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(s(mark(X))) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(fib1(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(fib(mark(X))) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(cons(mark(X1), X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(add(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(0) :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 s(z) -{ 1 }-> s(X) :|: z = 1 + X, X >= 0 s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 sel(z, z') -{ 1 }-> sel(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 sel(z, z') -{ 1 }-> sel(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 sel(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_fib(z0) -> fib(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) encode_fib1(z0, z1) -> fib1(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_0 -> 0 encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_add(z0, z1) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(0) -> c ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c9(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_FIB(z0) -> c10(FIB(encArg(z0)), ENCARG(z0)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_SEL(z0, z1) -> c12(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_FIB1(z0, z1) -> c13(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c14(S(encArg(z0)), ENCARG(z0)) ENCODE_0 -> c15 ENCODE_CONS(z0, z1) -> c16(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ADD(z0, z1) -> c17(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0)), S(0), S(0)) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), CONS(z0, fib1(z1, add(z0, z1))), FIB1(z1, add(z0, z1)), ADD(z0, z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), S(add(z0, z1)), ADD(z0, z1)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(0) -> c28(ACTIVE(0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) S tuples: ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0)), S(0), S(0)) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), CONS(z0, fib1(z1, add(z0, z1))), FIB1(z1, add(z0, z1)), ADD(z0, z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), S(add(z0, z1)), ADD(z0, z1)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(0) -> c28(ACTIVE(0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2, encArg_1, encode_active_1, encode_fib_1, encode_mark_1, encode_sel_2, encode_fib1_2, encode_s_1, encode_0, encode_cons_2, encode_add_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_0, ENCODE_CONS_2, ENCODE_ADD_2, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2 Compound Symbols: c, c1_2, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c9_2, c10_2, c11_2, c12_3, c13_3, c14_2, c15, c16_3, c17_3, c18_5, c19_4, c20_1, c21_3, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c28_1, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_0 -> c15 ENCARG(0) -> c ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_fib(z0) -> fib(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) encode_fib1(z0, z1) -> fib1(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_0 -> 0 encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_add(z0, z1) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c9(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_FIB(z0) -> c10(FIB(encArg(z0)), ENCARG(z0)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_SEL(z0, z1) -> c12(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_FIB1(z0, z1) -> c13(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c14(S(encArg(z0)), ENCARG(z0)) ENCODE_CONS(z0, z1) -> c16(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ADD(z0, z1) -> c17(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0)), S(0), S(0)) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), CONS(z0, fib1(z1, add(z0, z1))), FIB1(z1, add(z0, z1)), ADD(z0, z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), S(add(z0, z1)), ADD(z0, z1)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(0) -> c28(ACTIVE(0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) S tuples: ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0)), S(0), S(0)) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), CONS(z0, fib1(z1, add(z0, z1))), FIB1(z1, add(z0, z1)), ADD(z0, z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), S(add(z0, z1)), ADD(z0, z1)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(0) -> c28(ACTIVE(0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2, encArg_1, encode_active_1, encode_fib_1, encode_mark_1, encode_sel_2, encode_fib1_2, encode_s_1, encode_0, encode_cons_2, encode_add_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2 Compound Symbols: c1_2, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c9_2, c10_2, c11_2, c12_3, c13_3, c14_2, c16_3, c17_3, c18_5, c19_4, c20_1, c21_3, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c28_1, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_fib(z0) -> fib(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) encode_fib1(z0, z1) -> fib1(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_0 -> 0 encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_add(z0, z1) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c9(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_FIB(z0) -> c10(FIB(encArg(z0)), ENCARG(z0)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_SEL(z0, z1) -> c12(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_FIB1(z0, z1) -> c13(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c14(S(encArg(z0)), ENCARG(z0)) ENCODE_CONS(z0, z1) -> c16(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ADD(z0, z1) -> c17(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2, encArg_1, encode_active_1, encode_fib_1, encode_mark_1, encode_sel_2, encode_fib1_2, encode_s_1, encode_0, encode_cons_2, encode_add_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2 Compound Symbols: c1_2, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c9_2, c10_2, c11_2, c12_3, c13_3, c14_2, c16_3, c17_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28 ---------------------------------------- (41) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_fib(z0) -> fib(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) encode_fib1(z0, z1) -> fib1(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_0 -> 0 encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_add(z0, z1) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_FIB(z0) -> c(ENCARG(z0)) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(ENCARG(z0)) ENCODE_SEL(z0, z1) -> c(ENCARG(z1)) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(ENCARG(z0)) ENCODE_FIB1(z0, z1) -> c(ENCARG(z1)) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_CONS(z0, z1) -> c(ENCARG(z0)) ENCODE_CONS(z0, z1) -> c(ENCARG(z1)) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ENCARG(z0)) ENCODE_ADD(z0, z1) -> c(ENCARG(z1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2, encArg_1, encode_active_1, encode_fib_1, encode_mark_1, encode_sel_2, encode_fib1_2, encode_s_1, encode_0, encode_cons_2, encode_add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c1_2, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 12 leading nodes: ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_FIB(z0) -> c(ENCARG(z0)) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_SEL(z0, z1) -> c(ENCARG(z0)) ENCODE_SEL(z0, z1) -> c(ENCARG(z1)) ENCODE_FIB1(z0, z1) -> c(ENCARG(z0)) ENCODE_FIB1(z0, z1) -> c(ENCARG(z1)) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_CONS(z0, z1) -> c(ENCARG(z0)) ENCODE_CONS(z0, z1) -> c(ENCARG(z1)) ENCODE_ADD(z0, z1) -> c(ENCARG(z0)) ENCODE_ADD(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_fib(z0) -> fib(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) encode_fib1(z0, z1) -> fib1(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_0 -> 0 encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_add(z0, z1) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2, encArg_1, encode_active_1, encode_fib_1, encode_mark_1, encode_sel_2, encode_fib1_2, encode_s_1, encode_0, encode_cons_2, encode_add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c1_2, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_active(z0) -> active(encArg(z0)) encode_fib(z0) -> fib(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) encode_fib1(z0, z1) -> fib1(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_0 -> 0 encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_add(z0, z1) -> add(encArg(z0), encArg(z1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c1_2, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(z0)) -> c1(ACTIVE(encArg(z0)), ENCARG(z0)) by ENCARG(cons_active(0)) -> c1(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(0)) -> c1(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_active(0)) -> c1(ACTIVE(0), ENCARG(0)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(z0)) -> c2(MARK(encArg(z0)), ENCARG(z0)) by ENCARG(cons_mark(0)) -> c2(MARK(0), ENCARG(0)) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0), ENCARG(0)) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c3_2, c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(z0)) -> c3(FIB(encArg(z0)), ENCARG(z0)) by ENCARG(cons_fib(0)) -> c3(FIB(0), ENCARG(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(0)) -> c3(FIB(0), ENCARG(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_fib(0)) -> c3(FIB(0), ENCARG(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c4_3, c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_sel(z0, z1)) -> c4(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c5_3, c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib1(z0, z1)) -> c5(FIB1(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c6_2, c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) by ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c7_3, c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_cons(z0, z1)) -> c7(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c8_3, c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_add(z0, z1)) -> c8(ADD(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c24_3, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(fib(z0)) -> c24(ACTIVE(fib(mark(z0))), FIB(mark(z0)), MARK(z0)) by MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c25_4, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(z0, z1)) -> c25(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c26_4, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(fib1(z0, z1)) -> c26(ACTIVE(fib1(mark(z0), mark(z1))), FIB1(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c27_3, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(s(z0)) -> c27(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) by MARK(s(z0)) -> c27(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(z0)) -> c27(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(z0)) -> c27(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c29_3, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(cons(z0, z1)) -> c29(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) by MARK(cons(z0, z1)) -> c29(ACTIVE(cons(z0, z1)), CONS(mark(z0), z1), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(z0, z1)), CONS(mark(z0), z1), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(ACTIVE(cons(z0, z1)), CONS(mark(z0), z1), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c30_4, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c30(ACTIVE(add(mark(z0), mark(z1))), ADD(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) by ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_FIB(z0) -> c(FIB(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_FIB(z0) -> c(FIB(encArg(z0))) by ENCODE_FIB(0) -> c(FIB(0)) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(0) -> c(FIB(0)) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_FIB(0) -> c(FIB(0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_MARK(z0) -> c(MARK(encArg(z0))) by ENCODE_MARK(0) -> c(MARK(0)) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(0) -> c(MARK(0)) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (105) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_MARK(0) -> c(MARK(0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) by ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_FIB1(z0, z1) -> c(FIB1(encArg(z0), encArg(z1))) by ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_S(z0) -> c(S(encArg(z0))) by ENCODE_S(0) -> c(S(0)) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(0) -> c(S(0)) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_S(0) -> c(S(0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_CONS_2, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) by ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCODE_ADD_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c_1, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_ADD(z0, z1) -> c(ADD(encArg(z0), encArg(z1))) by ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_active(z0))) -> c1(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) by ENCARG(cons_active(cons_active(0))) -> c1(ACTIVE(active(0)), ENCARG(cons_active(0))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(0))) -> c1(ACTIVE(active(0)), ENCARG(cons_active(0))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_active(cons_active(0))) -> c1(ACTIVE(active(0)), ENCARG(cons_active(0))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_mark(z0))) -> c1(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) by ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1 ---------------------------------------- (125) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_sel(z0, z1))) -> c1(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) by ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_s(z0))) -> c1(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) by ENCARG(cons_active(cons_s(0))) -> c1(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(0))) -> c1(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_active(cons_s(0))) -> c1(ACTIVE(s(0)), ENCARG(cons_s(0))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_cons(z0, z1))) -> c1(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) by ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_add(z0, z1))) -> c1(ACTIVE(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) by ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_active(z0))) -> c2(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) by ENCARG(cons_mark(cons_active(0))) -> c2(MARK(active(0)), ENCARG(cons_active(0))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(0))) -> c2(MARK(active(0)), ENCARG(cons_active(0))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_mark(cons_active(0))) -> c2(MARK(active(0)), ENCARG(cons_active(0))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_mark(z0))) -> c2(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) by ENCARG(cons_mark(cons_mark(0))) -> c2(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c2(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1 ---------------------------------------- (143) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(cons_fib(z0))) -> c3(FIB(fib(encArg(z0))), ENCARG(cons_fib(z0))) by ENCARG(cons_fib(cons_fib(0))) -> c3(FIB(fib(0)), ENCARG(cons_fib(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(0))) -> c3(FIB(fib(0)), ENCARG(cons_fib(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_fib(cons_fib(0))) -> c3(FIB(fib(0)), ENCARG(cons_fib(0))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(cons_sel(z0, z1))) -> c3(FIB(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) by ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(cons_fib1(z0, z1))) -> c3(FIB(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) by ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(cons_s(z0))) -> c3(FIB(s(encArg(z0))), ENCARG(cons_s(z0))) by ENCARG(cons_fib(cons_s(0))) -> c3(FIB(s(0)), ENCARG(cons_s(0))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_s(0))) -> c3(FIB(s(0)), ENCARG(cons_s(0))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_fib(cons_s(0))) -> c3(FIB(s(0)), ENCARG(cons_s(0))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(cons_cons(z0, z1))) -> c3(FIB(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) by ENCARG(cons_fib(cons_cons(x0, 0))) -> c3(FIB(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_fib(cons_cons(x0, cons_active(z0)))) -> c3(FIB(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_mark(z0)))) -> c3(FIB(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_fib(z0)))) -> c3(FIB(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_sel(z0, z1)))) -> c3(FIB(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_fib1(z0, z1)))) -> c3(FIB(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_s(z0)))) -> c3(FIB(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_cons(z0, z1)))) -> c3(FIB(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_add(z0, z1)))) -> c3(FIB(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(0, x1))) -> c3(FIB(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_fib(cons_cons(cons_active(z0), x1))) -> c3(FIB(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_fib(cons_cons(cons_mark(z0), x1))) -> c3(FIB(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_fib(cons_cons(cons_fib(z0), x1))) -> c3(FIB(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_fib(cons_cons(cons_sel(z0, z1), x1))) -> c3(FIB(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_fib1(z0, z1), x1))) -> c3(FIB(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_s(z0), x1))) -> c3(FIB(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_fib(cons_cons(cons_cons(z0, z1), x1))) -> c3(FIB(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_add(z0, z1), x1))) -> c3(FIB(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, 0))) -> c3(FIB(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_fib(cons_cons(x0, cons_active(z0)))) -> c3(FIB(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_mark(z0)))) -> c3(FIB(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_fib(z0)))) -> c3(FIB(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_sel(z0, z1)))) -> c3(FIB(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_fib1(z0, z1)))) -> c3(FIB(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_s(z0)))) -> c3(FIB(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_cons(z0, z1)))) -> c3(FIB(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_add(z0, z1)))) -> c3(FIB(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(0, x1))) -> c3(FIB(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_fib(cons_cons(cons_active(z0), x1))) -> c3(FIB(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_fib(cons_cons(cons_mark(z0), x1))) -> c3(FIB(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_fib(cons_cons(cons_fib(z0), x1))) -> c3(FIB(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_fib(cons_cons(cons_sel(z0, z1), x1))) -> c3(FIB(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_fib1(z0, z1), x1))) -> c3(FIB(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_s(z0), x1))) -> c3(FIB(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_fib(cons_cons(cons_cons(z0, z1), x1))) -> c3(FIB(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_add(z0, z1), x1))) -> c3(FIB(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_fib(cons_add(z0, z1))) -> c3(FIB(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) by ENCARG(cons_fib(cons_add(x0, 0))) -> c3(FIB(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_fib(cons_add(x0, cons_active(z0)))) -> c3(FIB(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_fib(cons_add(x0, cons_mark(z0)))) -> c3(FIB(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_add(x0, cons_fib(z0)))) -> c3(FIB(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_add(x0, cons_sel(z0, z1)))) -> c3(FIB(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_fib1(z0, z1)))) -> c3(FIB(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_s(z0)))) -> c3(FIB(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_fib(cons_add(x0, cons_cons(z0, z1)))) -> c3(FIB(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_add(z0, z1)))) -> c3(FIB(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_add(0, x1))) -> c3(FIB(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_fib(cons_add(cons_active(z0), x1))) -> c3(FIB(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_fib(cons_add(cons_mark(z0), x1))) -> c3(FIB(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_fib(cons_add(cons_fib(z0), x1))) -> c3(FIB(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_fib(cons_add(cons_sel(z0, z1), x1))) -> c3(FIB(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_fib1(z0, z1), x1))) -> c3(FIB(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_s(z0), x1))) -> c3(FIB(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_fib(cons_add(cons_cons(z0, z1), x1))) -> c3(FIB(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_add(z0, z1), x1))) -> c3(FIB(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, 0))) -> c3(FIB(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_fib(cons_cons(x0, cons_active(z0)))) -> c3(FIB(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_mark(z0)))) -> c3(FIB(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_fib(z0)))) -> c3(FIB(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_sel(z0, z1)))) -> c3(FIB(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_fib1(z0, z1)))) -> c3(FIB(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_s(z0)))) -> c3(FIB(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_cons(z0, z1)))) -> c3(FIB(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_add(z0, z1)))) -> c3(FIB(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(0, x1))) -> c3(FIB(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_fib(cons_cons(cons_active(z0), x1))) -> c3(FIB(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_fib(cons_cons(cons_mark(z0), x1))) -> c3(FIB(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_fib(cons_cons(cons_fib(z0), x1))) -> c3(FIB(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_fib(cons_cons(cons_sel(z0, z1), x1))) -> c3(FIB(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_fib1(z0, z1), x1))) -> c3(FIB(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_s(z0), x1))) -> c3(FIB(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_fib(cons_cons(cons_cons(z0, z1), x1))) -> c3(FIB(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_add(z0, z1), x1))) -> c3(FIB(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_add(x0, 0))) -> c3(FIB(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_fib(cons_add(x0, cons_active(z0)))) -> c3(FIB(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_fib(cons_add(x0, cons_mark(z0)))) -> c3(FIB(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_add(x0, cons_fib(z0)))) -> c3(FIB(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_add(x0, cons_sel(z0, z1)))) -> c3(FIB(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_fib1(z0, z1)))) -> c3(FIB(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_s(z0)))) -> c3(FIB(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_fib(cons_add(x0, cons_cons(z0, z1)))) -> c3(FIB(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_add(z0, z1)))) -> c3(FIB(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_add(0, x1))) -> c3(FIB(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_fib(cons_add(cons_active(z0), x1))) -> c3(FIB(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_fib(cons_add(cons_mark(z0), x1))) -> c3(FIB(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_fib(cons_add(cons_fib(z0), x1))) -> c3(FIB(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_fib(cons_add(cons_sel(z0, z1), x1))) -> c3(FIB(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_fib1(z0, z1), x1))) -> c3(FIB(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_s(z0), x1))) -> c3(FIB(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_fib(cons_add(cons_cons(z0, z1), x1))) -> c3(FIB(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_add(z0, z1), x1))) -> c3(FIB(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_sel(x0, cons_fib(z0))) -> c4(SEL(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) by ENCARG(cons_sel(x0, cons_fib(0))) -> c4(SEL(encArg(x0), fib(0)), ENCARG(x0), ENCARG(cons_fib(0))) ENCARG(cons_sel(x0, cons_fib(cons_active(z0)))) -> c4(SEL(encArg(x0), fib(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_mark(z0)))) -> c4(SEL(encArg(x0), fib(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_fib(z0)))) -> c4(SEL(encArg(x0), fib(fib(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_sel(z0, z1)))) -> c4(SEL(encArg(x0), fib(sel(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_fib1(z0, z1)))) -> c4(SEL(encArg(x0), fib(fib1(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_s(z0)))) -> c4(SEL(encArg(x0), fib(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_cons(z0, z1)))) -> c4(SEL(encArg(x0), fib(cons(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_add(z0, z1)))) -> c4(SEL(encArg(x0), fib(add(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_sel(0, cons_fib(x1))) -> c4(SEL(0, fib(encArg(x1))), ENCARG(0), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_active(z0), cons_fib(x1))) -> c4(SEL(active(encArg(z0)), fib(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_mark(z0), cons_fib(x1))) -> c4(SEL(mark(encArg(z0)), fib(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_fib(z0), cons_fib(x1))) -> c4(SEL(fib(encArg(z0)), fib(encArg(x1))), ENCARG(cons_fib(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_sel(z0, z1), cons_fib(x1))) -> c4(SEL(sel(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_sel(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_fib1(z0, z1), cons_fib(x1))) -> c4(SEL(fib1(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_fib1(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_s(z0), cons_fib(x1))) -> c4(SEL(s(encArg(z0)), fib(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_cons(z0, z1), cons_fib(x1))) -> c4(SEL(cons(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_cons(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_add(z0, z1), cons_fib(x1))) -> c4(SEL(add(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_add(z0, z1)), ENCARG(cons_fib(x1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, 0))) -> c3(FIB(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_fib(cons_cons(x0, cons_active(z0)))) -> c3(FIB(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_mark(z0)))) -> c3(FIB(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_fib(z0)))) -> c3(FIB(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_sel(z0, z1)))) -> c3(FIB(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_fib1(z0, z1)))) -> c3(FIB(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_s(z0)))) -> c3(FIB(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_cons(z0, z1)))) -> c3(FIB(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_add(z0, z1)))) -> c3(FIB(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(0, x1))) -> c3(FIB(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_fib(cons_cons(cons_active(z0), x1))) -> c3(FIB(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_fib(cons_cons(cons_mark(z0), x1))) -> c3(FIB(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_fib(cons_cons(cons_fib(z0), x1))) -> c3(FIB(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_fib(cons_cons(cons_sel(z0, z1), x1))) -> c3(FIB(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_fib1(z0, z1), x1))) -> c3(FIB(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_s(z0), x1))) -> c3(FIB(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_fib(cons_cons(cons_cons(z0, z1), x1))) -> c3(FIB(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_add(z0, z1), x1))) -> c3(FIB(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_add(x0, 0))) -> c3(FIB(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_fib(cons_add(x0, cons_active(z0)))) -> c3(FIB(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_fib(cons_add(x0, cons_mark(z0)))) -> c3(FIB(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_add(x0, cons_fib(z0)))) -> c3(FIB(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_add(x0, cons_sel(z0, z1)))) -> c3(FIB(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_fib1(z0, z1)))) -> c3(FIB(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_s(z0)))) -> c3(FIB(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_fib(cons_add(x0, cons_cons(z0, z1)))) -> c3(FIB(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_add(z0, z1)))) -> c3(FIB(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_add(0, x1))) -> c3(FIB(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_fib(cons_add(cons_active(z0), x1))) -> c3(FIB(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_fib(cons_add(cons_mark(z0), x1))) -> c3(FIB(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_fib(cons_add(cons_fib(z0), x1))) -> c3(FIB(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_fib(cons_add(cons_sel(z0, z1), x1))) -> c3(FIB(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_fib1(z0, z1), x1))) -> c3(FIB(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_s(z0), x1))) -> c3(FIB(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_fib(cons_add(cons_cons(z0, z1), x1))) -> c3(FIB(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_add(z0, z1), x1))) -> c3(FIB(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_sel(x0, cons_fib(0))) -> c4(SEL(encArg(x0), fib(0)), ENCARG(x0), ENCARG(cons_fib(0))) ENCARG(cons_sel(x0, cons_fib(cons_active(z0)))) -> c4(SEL(encArg(x0), fib(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_mark(z0)))) -> c4(SEL(encArg(x0), fib(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_fib(z0)))) -> c4(SEL(encArg(x0), fib(fib(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_sel(z0, z1)))) -> c4(SEL(encArg(x0), fib(sel(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_fib1(z0, z1)))) -> c4(SEL(encArg(x0), fib(fib1(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_s(z0)))) -> c4(SEL(encArg(x0), fib(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_cons(z0, z1)))) -> c4(SEL(encArg(x0), fib(cons(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_add(z0, z1)))) -> c4(SEL(encArg(x0), fib(add(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_sel(0, cons_fib(x1))) -> c4(SEL(0, fib(encArg(x1))), ENCARG(0), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_active(z0), cons_fib(x1))) -> c4(SEL(active(encArg(z0)), fib(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_mark(z0), cons_fib(x1))) -> c4(SEL(mark(encArg(z0)), fib(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_fib(z0), cons_fib(x1))) -> c4(SEL(fib(encArg(z0)), fib(encArg(x1))), ENCARG(cons_fib(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_sel(z0, z1), cons_fib(x1))) -> c4(SEL(sel(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_sel(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_fib1(z0, z1), cons_fib(x1))) -> c4(SEL(fib1(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_fib1(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_s(z0), cons_fib(x1))) -> c4(SEL(s(encArg(z0)), fib(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_cons(z0, z1), cons_fib(x1))) -> c4(SEL(cons(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_cons(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_add(z0, z1), cons_fib(x1))) -> c4(SEL(add(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_add(z0, z1)), ENCARG(cons_fib(x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_fib(z0)) -> fib(encArg(z0)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encArg(cons_fib1(z0, z1)) -> fib1(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_add(z0, z1)) -> add(encArg(z0), encArg(z1)) active(fib(z0)) -> mark(sel(z0, fib1(s(0), s(0)))) active(fib1(z0, z1)) -> mark(cons(z0, fib1(z1, add(z0, z1)))) active(add(0, z0)) -> mark(z0) active(add(s(z0), z1)) -> mark(s(add(z0, z1))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(fib(z0)) -> active(fib(mark(z0))) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) mark(fib1(z0, z1)) -> active(fib1(mark(z0), mark(z1))) mark(s(z0)) -> active(s(mark(z0))) mark(0) -> active(0) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(add(z0, z1)) -> active(add(mark(z0), mark(z1))) fib(mark(z0)) -> fib(z0) fib(active(z0)) -> fib(z0) sel(mark(z0), z1) -> sel(z0, z1) sel(z0, mark(z1)) -> sel(z0, z1) sel(active(z0), z1) -> sel(z0, z1) sel(z0, active(z1)) -> sel(z0, z1) fib1(mark(z0), z1) -> fib1(z0, z1) fib1(z0, mark(z1)) -> fib1(z0, z1) fib1(active(z0), z1) -> fib1(z0, z1) fib1(z0, active(z1)) -> fib1(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) cons(mark(z0), z1) -> cons(z0, z1) cons(z0, mark(z1)) -> cons(z0, z1) cons(active(z0), z1) -> cons(z0, z1) cons(z0, active(z1)) -> cons(z0, z1) add(mark(z0), z1) -> add(z0, z1) add(z0, mark(z1)) -> add(z0, z1) add(active(z0), z1) -> add(z0, z1) add(z0, active(z1)) -> add(z0, z1) Tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 ENCARG(cons_active(cons_fib(z0))) -> c1(ACTIVE(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_active(cons_fib1(z0, z1))) -> c1(ACTIVE(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_fib(z0))) -> c2(MARK(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c2(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_fib1(z0, z1))) -> c2(MARK(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c2(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c2(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_add(z0, z1))) -> c2(MARK(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_mark(0)) -> c2(MARK(0)) ENCARG(cons_fib(cons_active(z0))) -> c3(FIB(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_fib(cons_mark(z0))) -> c3(FIB(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_active(z0))) -> c4(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c4(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c4(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(x0, cons_fib1(z0, z1))) -> c4(SEL(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c4(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c4(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_add(z0, z1))) -> c4(SEL(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c4(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c4(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_fib(z0), x1)) -> c4(SEL(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c4(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_fib1(z0, z1), x1)) -> c4(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c4(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c4(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_add(z0, z1), x1)) -> c4(SEL(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c4(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c4(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_fib1(x0, cons_active(z0))) -> c5(FIB1(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_fib1(x0, cons_mark(z0))) -> c5(FIB1(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_fib1(x0, cons_fib(z0))) -> c5(FIB1(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_fib1(x0, cons_sel(z0, z1))) -> c5(FIB1(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_fib1(x0, cons_fib1(z0, z1))) -> c5(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_fib1(x0, cons_s(z0))) -> c5(FIB1(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_fib1(x0, cons_cons(z0, z1))) -> c5(FIB1(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_fib1(x0, cons_add(z0, z1))) -> c5(FIB1(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_fib1(cons_active(z0), x1)) -> c5(FIB1(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_mark(z0), x1)) -> c5(FIB1(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib(z0), x1)) -> c5(FIB1(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_sel(z0, z1), x1)) -> c5(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_fib1(z0, z1), x1)) -> c5(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_s(z0), x1)) -> c5(FIB1(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_fib1(cons_cons(z0, z1), x1)) -> c5(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(cons_add(z0, z1), x1)) -> c5(FIB1(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_fib1(x0, 0)) -> c5(FIB1(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_fib1(0, x1)) -> c5(FIB1(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_fib(z0))) -> c6(S(fib(encArg(z0))), ENCARG(cons_fib(z0))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_s(cons_fib1(z0, z1))) -> c6(S(fib1(encArg(z0), encArg(z1))), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_add(z0, z1))) -> c6(S(add(encArg(z0), encArg(z1))), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c7(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c7(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_fib(z0))) -> c7(CONS(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c7(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_fib1(z0, z1))) -> c7(CONS(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c7(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c7(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_add(z0, z1))) -> c7(CONS(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c7(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c7(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_fib(z0), x1)) -> c7(CONS(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c7(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_fib1(z0, z1), x1)) -> c7(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c7(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c7(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_add(z0, z1), x1)) -> c7(CONS(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c7(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c7(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_add(x0, cons_active(z0))) -> c8(ADD(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_add(x0, cons_mark(z0))) -> c8(ADD(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_add(x0, cons_fib(z0))) -> c8(ADD(encArg(x0), fib(encArg(z0))), ENCARG(x0), ENCARG(cons_fib(z0))) ENCARG(cons_add(x0, cons_sel(z0, z1))) -> c8(ADD(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_add(x0, cons_fib1(z0, z1))) -> c8(ADD(encArg(x0), fib1(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_fib1(z0, z1))) ENCARG(cons_add(x0, cons_s(z0))) -> c8(ADD(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_add(x0, cons_cons(z0, z1))) -> c8(ADD(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_add(x0, cons_add(z0, z1))) -> c8(ADD(encArg(x0), add(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_add(z0, z1))) ENCARG(cons_add(cons_active(z0), x1)) -> c8(ADD(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_add(cons_mark(z0), x1)) -> c8(ADD(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_add(cons_fib(z0), x1)) -> c8(ADD(fib(encArg(z0)), encArg(x1)), ENCARG(cons_fib(z0)), ENCARG(x1)) ENCARG(cons_add(cons_sel(z0, z1), x1)) -> c8(ADD(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_fib1(z0, z1), x1)) -> c8(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_fib1(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_s(z0), x1)) -> c8(ADD(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_add(cons_cons(z0, z1), x1)) -> c8(ADD(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_add(cons_add(z0, z1), x1)) -> c8(ADD(add(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_add(z0, z1)), ENCARG(x1)) ENCARG(cons_add(x0, 0)) -> c8(ADD(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_add(0, x1)) -> c8(ADD(0, encArg(x1)), ENCARG(x1)) MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_fib(z0)) -> c(ACTIVE(fib(encArg(z0)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_fib1(z0, z1)) -> c(ACTIVE(fib1(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_add(z0, z1)) -> c(ACTIVE(add(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_active(z0)) -> c(FIB(active(encArg(z0)))) ENCODE_FIB(cons_mark(z0)) -> c(FIB(mark(encArg(z0)))) ENCODE_FIB(cons_fib(z0)) -> c(FIB(fib(encArg(z0)))) ENCODE_FIB(cons_sel(z0, z1)) -> c(FIB(sel(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_fib1(z0, z1)) -> c(FIB(fib1(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_s(z0)) -> c(FIB(s(encArg(z0)))) ENCODE_FIB(cons_cons(z0, z1)) -> c(FIB(cons(encArg(z0), encArg(z1)))) ENCODE_FIB(cons_add(z0, z1)) -> c(FIB(add(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_fib(z0)) -> c(MARK(fib(encArg(z0)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_fib1(z0, z1)) -> c(MARK(fib1(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_add(z0, z1)) -> c(MARK(add(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, cons_active(z0)) -> c(SEL(encArg(x0), active(encArg(z0)))) ENCODE_SEL(x0, cons_mark(z0)) -> c(SEL(encArg(x0), mark(encArg(z0)))) ENCODE_SEL(x0, cons_fib(z0)) -> c(SEL(encArg(x0), fib(encArg(z0)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_fib1(z0, z1)) -> c(SEL(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_add(z0, z1)) -> c(SEL(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(cons_active(z0), x1) -> c(SEL(active(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_mark(z0), x1) -> c(SEL(mark(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_fib(z0), x1) -> c(SEL(fib(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_fib1(z0, z1), x1) -> c(SEL(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_add(z0, z1), x1) -> c(SEL(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(x0, 0) -> c(FIB1(encArg(x0), 0)) ENCODE_FIB1(x0, cons_active(z0)) -> c(FIB1(encArg(x0), active(encArg(z0)))) ENCODE_FIB1(x0, cons_mark(z0)) -> c(FIB1(encArg(x0), mark(encArg(z0)))) ENCODE_FIB1(x0, cons_fib(z0)) -> c(FIB1(encArg(x0), fib(encArg(z0)))) ENCODE_FIB1(x0, cons_sel(z0, z1)) -> c(FIB1(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_fib1(z0, z1)) -> c(FIB1(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_s(z0)) -> c(FIB1(encArg(x0), s(encArg(z0)))) ENCODE_FIB1(x0, cons_cons(z0, z1)) -> c(FIB1(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_FIB1(x0, cons_add(z0, z1)) -> c(FIB1(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_FIB1(0, x1) -> c(FIB1(0, encArg(x1))) ENCODE_FIB1(cons_active(z0), x1) -> c(FIB1(active(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_mark(z0), x1) -> c(FIB1(mark(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_fib(z0), x1) -> c(FIB1(fib(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_sel(z0, z1), x1) -> c(FIB1(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_fib1(z0, z1), x1) -> c(FIB1(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_s(z0), x1) -> c(FIB1(s(encArg(z0)), encArg(x1))) ENCODE_FIB1(cons_cons(z0, z1), x1) -> c(FIB1(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_FIB1(cons_add(z0, z1), x1) -> c(FIB1(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_fib(z0)) -> c(S(fib(encArg(z0)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_S(cons_fib1(z0, z1)) -> c(S(fib1(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_add(z0, z1)) -> c(S(add(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, cons_active(z0)) -> c(CONS(encArg(x0), active(encArg(z0)))) ENCODE_CONS(x0, cons_mark(z0)) -> c(CONS(encArg(x0), mark(encArg(z0)))) ENCODE_CONS(x0, cons_fib(z0)) -> c(CONS(encArg(x0), fib(encArg(z0)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_fib1(z0, z1)) -> c(CONS(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_add(z0, z1)) -> c(CONS(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(cons_active(z0), x1) -> c(CONS(active(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_mark(z0), x1) -> c(CONS(mark(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_fib(z0), x1) -> c(CONS(fib(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_fib1(z0, z1), x1) -> c(CONS(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_add(z0, z1), x1) -> c(CONS(add(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(x0, 0) -> c(ADD(encArg(x0), 0)) ENCODE_ADD(x0, cons_active(z0)) -> c(ADD(encArg(x0), active(encArg(z0)))) ENCODE_ADD(x0, cons_mark(z0)) -> c(ADD(encArg(x0), mark(encArg(z0)))) ENCODE_ADD(x0, cons_fib(z0)) -> c(ADD(encArg(x0), fib(encArg(z0)))) ENCODE_ADD(x0, cons_sel(z0, z1)) -> c(ADD(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_fib1(z0, z1)) -> c(ADD(encArg(x0), fib1(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_s(z0)) -> c(ADD(encArg(x0), s(encArg(z0)))) ENCODE_ADD(x0, cons_cons(z0, z1)) -> c(ADD(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_ADD(x0, cons_add(z0, z1)) -> c(ADD(encArg(x0), add(encArg(z0), encArg(z1)))) ENCODE_ADD(0, x1) -> c(ADD(0, encArg(x1))) ENCODE_ADD(cons_active(z0), x1) -> c(ADD(active(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_mark(z0), x1) -> c(ADD(mark(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_fib(z0), x1) -> c(ADD(fib(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_sel(z0, z1), x1) -> c(ADD(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_fib1(z0, z1), x1) -> c(ADD(fib1(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_s(z0), x1) -> c(ADD(s(encArg(z0)), encArg(x1))) ENCODE_ADD(cons_cons(z0, z1), x1) -> c(ADD(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_ADD(cons_add(z0, z1), x1) -> c(ADD(add(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c1(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c1(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_fib(z0)))) -> c1(ACTIVE(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c1(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_active(cons_fib1(z0, z1)))) -> c1(ACTIVE(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c1(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c1(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_add(z0, z1)))) -> c1(ACTIVE(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c1(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c1(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_fib(z0)))) -> c1(ACTIVE(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c1(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_fib1(z0, z1)))) -> c1(ACTIVE(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c1(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c1(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_add(z0, z1)))) -> c1(ACTIVE(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c9(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c9(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_sel(x0, 0))) -> c1(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c1(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c1(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_fib(z0)))) -> c1(ACTIVE(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c1(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_add(z0, z1)))) -> c1(ACTIVE(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c1(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c1(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c1(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_fib(z0), x1))) -> c1(ACTIVE(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c1(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c1(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c1(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_add(z0, z1), x1))) -> c1(ACTIVE(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c1(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c1(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_fib(z0)))) -> c1(ACTIVE(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c1(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_s(cons_fib1(z0, z1)))) -> c1(ACTIVE(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c1(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c1(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_add(z0, z1)))) -> c1(ACTIVE(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(x0, 0))) -> c1(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c1(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c1(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_fib(z0)))) -> c1(ACTIVE(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c1(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_add(z0, z1)))) -> c1(ACTIVE(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c1(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c1(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c1(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_fib(z0), x1))) -> c1(ACTIVE(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c1(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c1(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c1(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_add(z0, z1), x1))) -> c1(ACTIVE(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_active(cons_add(x0, 0))) -> c1(ACTIVE(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_active(cons_add(x0, cons_active(z0)))) -> c1(ACTIVE(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_active(cons_add(x0, cons_mark(z0)))) -> c1(ACTIVE(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_active(cons_add(x0, cons_fib(z0)))) -> c1(ACTIVE(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_active(cons_add(x0, cons_sel(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_fib1(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_s(z0)))) -> c1(ACTIVE(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_active(cons_add(x0, cons_cons(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_add(x0, cons_add(z0, z1)))) -> c1(ACTIVE(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_active(cons_add(0, x1))) -> c1(ACTIVE(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_active(cons_add(cons_active(z0), x1))) -> c1(ACTIVE(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_active(cons_add(cons_mark(z0), x1))) -> c1(ACTIVE(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_active(cons_add(cons_fib(z0), x1))) -> c1(ACTIVE(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_active(cons_add(cons_sel(z0, z1), x1))) -> c1(ACTIVE(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_fib1(z0, z1), x1))) -> c1(ACTIVE(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_s(z0), x1))) -> c1(ACTIVE(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_active(cons_add(cons_cons(z0, z1), x1))) -> c1(ACTIVE(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_add(cons_add(z0, z1), x1))) -> c1(ACTIVE(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c2(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c2(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_fib(z0)))) -> c2(MARK(active(fib(encArg(z0)))), ENCARG(cons_active(cons_fib(z0)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c2(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_active(cons_fib1(z0, z1)))) -> c2(MARK(active(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c2(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c2(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_add(z0, z1)))) -> c2(MARK(active(add(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c2(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c2(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_fib(z0)))) -> c2(MARK(mark(fib(encArg(z0)))), ENCARG(cons_mark(cons_fib(z0)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c2(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_fib1(z0, z1)))) -> c2(MARK(mark(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_fib1(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c2(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c2(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_add(z0, z1)))) -> c2(MARK(mark(add(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_add(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_fib(cons_fib(cons_active(z0)))) -> c3(FIB(fib(active(encArg(z0)))), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_fib(cons_fib(cons_mark(z0)))) -> c3(FIB(fib(mark(encArg(z0)))), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_fib(cons_fib(cons_fib(z0)))) -> c3(FIB(fib(fib(encArg(z0)))), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_fib(cons_fib(cons_sel(z0, z1)))) -> c3(FIB(fib(sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_fib1(z0, z1)))) -> c3(FIB(fib(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_s(z0)))) -> c3(FIB(fib(s(encArg(z0)))), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_fib(cons_fib(cons_cons(z0, z1)))) -> c3(FIB(fib(cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib(cons_add(z0, z1)))) -> c3(FIB(fib(add(encArg(z0), encArg(z1)))), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, 0))) -> c3(FIB(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_fib(cons_sel(x0, cons_active(z0)))) -> c3(FIB(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_mark(z0)))) -> c3(FIB(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_fib(z0)))) -> c3(FIB(sel(encArg(x0), fib(encArg(z0)))), ENCARG(cons_sel(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_sel(z0, z1)))) -> c3(FIB(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_fib1(z0, z1)))) -> c3(FIB(sel(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_s(z0)))) -> c3(FIB(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_fib(cons_sel(x0, cons_cons(z0, z1)))) -> c3(FIB(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_sel(x0, cons_add(z0, z1)))) -> c3(FIB(sel(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_sel(0, x1))) -> c3(FIB(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_fib(cons_sel(cons_active(z0), x1))) -> c3(FIB(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_fib(cons_sel(cons_mark(z0), x1))) -> c3(FIB(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_fib(cons_sel(cons_fib(z0), x1))) -> c3(FIB(sel(fib(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_fib(z0), x1))) ENCARG(cons_fib(cons_sel(cons_sel(z0, z1), x1))) -> c3(FIB(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_fib1(z0, z1), x1))) -> c3(FIB(sel(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_s(z0), x1))) -> c3(FIB(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_fib(cons_sel(cons_cons(z0, z1), x1))) -> c3(FIB(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_sel(cons_add(z0, z1), x1))) -> c3(FIB(sel(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(x0, 0))) -> c3(FIB(fib1(encArg(x0), 0)), ENCARG(cons_fib1(x0, 0))) ENCARG(cons_fib(cons_fib1(x0, cons_active(z0)))) -> c3(FIB(fib1(encArg(x0), active(encArg(z0)))), ENCARG(cons_fib1(x0, cons_active(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_mark(z0)))) -> c3(FIB(fib1(encArg(x0), mark(encArg(z0)))), ENCARG(cons_fib1(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib(z0)))) -> c3(FIB(fib1(encArg(x0), fib(encArg(z0)))), ENCARG(cons_fib1(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_sel(z0, z1)))) -> c3(FIB(fib1(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_fib1(z0, z1)))) -> c3(FIB(fib1(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_s(z0)))) -> c3(FIB(fib1(encArg(x0), s(encArg(z0)))), ENCARG(cons_fib1(x0, cons_s(z0)))) ENCARG(cons_fib(cons_fib1(x0, cons_cons(z0, z1)))) -> c3(FIB(fib1(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_fib1(x0, cons_add(z0, z1)))) -> c3(FIB(fib1(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_fib1(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_fib1(0, x1))) -> c3(FIB(fib1(0, encArg(x1))), ENCARG(cons_fib1(0, x1))) ENCARG(cons_fib(cons_fib1(cons_active(z0), x1))) -> c3(FIB(fib1(active(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_active(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_mark(z0), x1))) -> c3(FIB(fib1(mark(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_mark(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_fib(z0), x1))) -> c3(FIB(fib1(fib(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_fib(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_sel(z0, z1), x1))) -> c3(FIB(fib1(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_fib1(z0, z1), x1))) -> c3(FIB(fib1(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_s(z0), x1))) -> c3(FIB(fib1(s(encArg(z0)), encArg(x1))), ENCARG(cons_fib1(cons_s(z0), x1))) ENCARG(cons_fib(cons_fib1(cons_cons(z0, z1), x1))) -> c3(FIB(fib1(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_fib1(cons_add(z0, z1), x1))) -> c3(FIB(fib1(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_fib1(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_s(cons_active(z0)))) -> c3(FIB(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_fib(cons_s(cons_mark(z0)))) -> c3(FIB(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_fib(cons_s(cons_fib(z0)))) -> c3(FIB(s(fib(encArg(z0)))), ENCARG(cons_s(cons_fib(z0)))) ENCARG(cons_fib(cons_s(cons_sel(z0, z1)))) -> c3(FIB(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_fib(cons_s(cons_fib1(z0, z1)))) -> c3(FIB(s(fib1(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_s(cons_s(z0)))) -> c3(FIB(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_fib(cons_s(cons_cons(z0, z1)))) -> c3(FIB(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_fib(cons_s(cons_add(z0, z1)))) -> c3(FIB(s(add(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, 0))) -> c3(FIB(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_fib(cons_cons(x0, cons_active(z0)))) -> c3(FIB(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_mark(z0)))) -> c3(FIB(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_fib(z0)))) -> c3(FIB(cons(encArg(x0), fib(encArg(z0)))), ENCARG(cons_cons(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_sel(z0, z1)))) -> c3(FIB(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_fib1(z0, z1)))) -> c3(FIB(cons(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_s(z0)))) -> c3(FIB(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_fib(cons_cons(x0, cons_cons(z0, z1)))) -> c3(FIB(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_cons(x0, cons_add(z0, z1)))) -> c3(FIB(cons(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_cons(0, x1))) -> c3(FIB(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_fib(cons_cons(cons_active(z0), x1))) -> c3(FIB(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_fib(cons_cons(cons_mark(z0), x1))) -> c3(FIB(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_fib(cons_cons(cons_fib(z0), x1))) -> c3(FIB(cons(fib(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_fib(z0), x1))) ENCARG(cons_fib(cons_cons(cons_sel(z0, z1), x1))) -> c3(FIB(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_fib1(z0, z1), x1))) -> c3(FIB(cons(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_s(z0), x1))) -> c3(FIB(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_fib(cons_cons(cons_cons(z0, z1), x1))) -> c3(FIB(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_cons(cons_add(z0, z1), x1))) -> c3(FIB(cons(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_add(z0, z1), x1))) ENCARG(cons_fib(cons_add(x0, 0))) -> c3(FIB(add(encArg(x0), 0)), ENCARG(cons_add(x0, 0))) ENCARG(cons_fib(cons_add(x0, cons_active(z0)))) -> c3(FIB(add(encArg(x0), active(encArg(z0)))), ENCARG(cons_add(x0, cons_active(z0)))) ENCARG(cons_fib(cons_add(x0, cons_mark(z0)))) -> c3(FIB(add(encArg(x0), mark(encArg(z0)))), ENCARG(cons_add(x0, cons_mark(z0)))) ENCARG(cons_fib(cons_add(x0, cons_fib(z0)))) -> c3(FIB(add(encArg(x0), fib(encArg(z0)))), ENCARG(cons_add(x0, cons_fib(z0)))) ENCARG(cons_fib(cons_add(x0, cons_sel(z0, z1)))) -> c3(FIB(add(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_sel(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_fib1(z0, z1)))) -> c3(FIB(add(encArg(x0), fib1(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_fib1(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_s(z0)))) -> c3(FIB(add(encArg(x0), s(encArg(z0)))), ENCARG(cons_add(x0, cons_s(z0)))) ENCARG(cons_fib(cons_add(x0, cons_cons(z0, z1)))) -> c3(FIB(add(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_cons(z0, z1)))) ENCARG(cons_fib(cons_add(x0, cons_add(z0, z1)))) -> c3(FIB(add(encArg(x0), add(encArg(z0), encArg(z1)))), ENCARG(cons_add(x0, cons_add(z0, z1)))) ENCARG(cons_fib(cons_add(0, x1))) -> c3(FIB(add(0, encArg(x1))), ENCARG(cons_add(0, x1))) ENCARG(cons_fib(cons_add(cons_active(z0), x1))) -> c3(FIB(add(active(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_active(z0), x1))) ENCARG(cons_fib(cons_add(cons_mark(z0), x1))) -> c3(FIB(add(mark(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_mark(z0), x1))) ENCARG(cons_fib(cons_add(cons_fib(z0), x1))) -> c3(FIB(add(fib(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_fib(z0), x1))) ENCARG(cons_fib(cons_add(cons_sel(z0, z1), x1))) -> c3(FIB(add(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_sel(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_fib1(z0, z1), x1))) -> c3(FIB(add(fib1(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_fib1(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_s(z0), x1))) -> c3(FIB(add(s(encArg(z0)), encArg(x1))), ENCARG(cons_add(cons_s(z0), x1))) ENCARG(cons_fib(cons_add(cons_cons(z0, z1), x1))) -> c3(FIB(add(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_cons(z0, z1), x1))) ENCARG(cons_fib(cons_add(cons_add(z0, z1), x1))) -> c3(FIB(add(add(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_add(cons_add(z0, z1), x1))) ENCARG(cons_sel(x0, cons_fib(cons_active(z0)))) -> c4(SEL(encArg(x0), fib(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_active(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_mark(z0)))) -> c4(SEL(encArg(x0), fib(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_mark(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_fib(z0)))) -> c4(SEL(encArg(x0), fib(fib(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_fib(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_sel(z0, z1)))) -> c4(SEL(encArg(x0), fib(sel(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_sel(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_fib1(z0, z1)))) -> c4(SEL(encArg(x0), fib(fib1(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_fib1(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_s(z0)))) -> c4(SEL(encArg(x0), fib(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_fib(cons_s(z0)))) ENCARG(cons_sel(x0, cons_fib(cons_cons(z0, z1)))) -> c4(SEL(encArg(x0), fib(cons(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_cons(z0, z1)))) ENCARG(cons_sel(x0, cons_fib(cons_add(z0, z1)))) -> c4(SEL(encArg(x0), fib(add(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_fib(cons_add(z0, z1)))) ENCARG(cons_sel(cons_active(z0), cons_fib(x1))) -> c4(SEL(active(encArg(z0)), fib(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_mark(z0), cons_fib(x1))) -> c4(SEL(mark(encArg(z0)), fib(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_fib(z0), cons_fib(x1))) -> c4(SEL(fib(encArg(z0)), fib(encArg(x1))), ENCARG(cons_fib(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_sel(z0, z1), cons_fib(x1))) -> c4(SEL(sel(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_sel(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_fib1(z0, z1), cons_fib(x1))) -> c4(SEL(fib1(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_fib1(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_s(z0), cons_fib(x1))) -> c4(SEL(s(encArg(z0)), fib(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_cons(z0, z1), cons_fib(x1))) -> c4(SEL(cons(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_cons(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(cons_add(z0, z1), cons_fib(x1))) -> c4(SEL(add(encArg(z0), encArg(z1)), fib(encArg(x1))), ENCARG(cons_add(z0, z1)), ENCARG(cons_fib(x1))) ENCARG(cons_sel(x0, cons_fib(0))) -> c4(SEL(encArg(x0), fib(0)), ENCARG(x0)) ENCARG(cons_sel(0, cons_fib(x1))) -> c4(SEL(0, fib(encArg(x1))), ENCARG(cons_fib(x1))) S tuples: ACTIVE(add(0, z0)) -> c20(MARK(z0)) ACTIVE(sel(0, cons(z0, z1))) -> c22(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c23(MARK(sel(z0, z2)), SEL(z0, z2)) FIB(mark(z0)) -> c31(FIB(z0)) FIB(active(z0)) -> c32(FIB(z0)) SEL(mark(z0), z1) -> c33(SEL(z0, z1)) SEL(z0, mark(z1)) -> c34(SEL(z0, z1)) SEL(active(z0), z1) -> c35(SEL(z0, z1)) SEL(z0, active(z1)) -> c36(SEL(z0, z1)) FIB1(mark(z0), z1) -> c37(FIB1(z0, z1)) FIB1(z0, mark(z1)) -> c38(FIB1(z0, z1)) FIB1(active(z0), z1) -> c39(FIB1(z0, z1)) FIB1(z0, active(z1)) -> c40(FIB1(z0, z1)) S(mark(z0)) -> c41(S(z0)) S(active(z0)) -> c42(S(z0)) CONS(mark(z0), z1) -> c43(CONS(z0, z1)) CONS(z0, mark(z1)) -> c44(CONS(z0, z1)) CONS(active(z0), z1) -> c45(CONS(z0, z1)) CONS(z0, active(z1)) -> c46(CONS(z0, z1)) ADD(mark(z0), z1) -> c47(ADD(z0, z1)) ADD(z0, mark(z1)) -> c48(ADD(z0, z1)) ADD(active(z0), z1) -> c49(ADD(z0, z1)) ADD(z0, active(z1)) -> c50(ADD(z0, z1)) ACTIVE(fib(z0)) -> c18(MARK(sel(z0, fib1(s(0), s(0)))), SEL(z0, fib1(s(0), s(0)))) ACTIVE(fib1(z0, z1)) -> c19(MARK(cons(z0, fib1(z1, add(z0, z1)))), ADD(z0, z1)) ACTIVE(add(s(z0), z1)) -> c21(MARK(s(add(z0, z1))), ADD(z0, z1)) MARK(0) -> c28 MARK(fib(z0)) -> c24(ACTIVE(fib(z0)), FIB(mark(z0)), MARK(z0)) MARK(fib(fib(z0))) -> c24(ACTIVE(fib(active(fib(mark(z0))))), FIB(mark(fib(z0))), MARK(fib(z0))) MARK(fib(sel(z0, z1))) -> c24(ACTIVE(fib(active(sel(mark(z0), mark(z1))))), FIB(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(fib(fib1(z0, z1))) -> c24(ACTIVE(fib(active(fib1(mark(z0), mark(z1))))), FIB(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(fib(s(z0))) -> c24(ACTIVE(fib(active(s(mark(z0))))), FIB(mark(s(z0))), MARK(s(z0))) MARK(fib(0)) -> c24(ACTIVE(fib(active(0))), FIB(mark(0)), MARK(0)) MARK(fib(cons(z0, z1))) -> c24(ACTIVE(fib(active(cons(mark(z0), z1)))), FIB(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(fib(add(z0, z1))) -> c24(ACTIVE(fib(active(add(mark(z0), mark(z1))))), FIB(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(sel(z0, x1)) -> c25(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c25(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, fib(z0))) -> c25(ACTIVE(sel(mark(x0), active(fib(mark(z0))))), SEL(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(sel(x0, sel(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(sel(mark(z0), mark(z1))))), SEL(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(sel(x0, fib1(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(fib1(mark(z0), mark(z1))))), SEL(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(sel(x0, s(z0))) -> c25(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, 0)) -> c25(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, cons(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(cons(mark(z0), z1)))), SEL(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(sel(x0, add(z0, z1))) -> c25(ACTIVE(sel(mark(x0), active(add(mark(z0), mark(z1))))), SEL(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(sel(fib(z0), x1)) -> c25(ACTIVE(sel(active(fib(mark(z0))), mark(x1))), SEL(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c25(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(fib1(z0, z1), x1)) -> c25(ACTIVE(sel(active(fib1(mark(z0), mark(z1))), mark(x1))), SEL(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c25(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(0, x1)) -> c25(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c25(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(add(z0, z1), x1)) -> c25(ACTIVE(sel(active(add(mark(z0), mark(z1))), mark(x1))), SEL(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(fib1(z0, x1)) -> c26(ACTIVE(fib1(z0, mark(x1))), FIB1(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(fib1(x0, z1)) -> c26(ACTIVE(fib1(mark(x0), z1)), FIB1(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(fib1(x0, fib(z0))) -> c26(ACTIVE(fib1(mark(x0), active(fib(mark(z0))))), FIB1(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(fib1(x0, sel(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(sel(mark(z0), mark(z1))))), FIB1(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(fib1(x0, fib1(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(fib1(mark(z0), mark(z1))))), FIB1(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(fib1(x0, s(z0))) -> c26(ACTIVE(fib1(mark(x0), active(s(mark(z0))))), FIB1(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(fib1(x0, 0)) -> c26(ACTIVE(fib1(mark(x0), active(0))), FIB1(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(fib1(x0, cons(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(cons(mark(z0), z1)))), FIB1(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(fib1(x0, add(z0, z1))) -> c26(ACTIVE(fib1(mark(x0), active(add(mark(z0), mark(z1))))), FIB1(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(fib1(fib(z0), x1)) -> c26(ACTIVE(fib1(active(fib(mark(z0))), mark(x1))), FIB1(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(fib1(sel(z0, z1), x1)) -> c26(ACTIVE(fib1(active(sel(mark(z0), mark(z1))), mark(x1))), FIB1(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(fib1(fib1(z0, z1), x1)) -> c26(ACTIVE(fib1(active(fib1(mark(z0), mark(z1))), mark(x1))), FIB1(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(fib1(s(z0), x1)) -> c26(ACTIVE(fib1(active(s(mark(z0))), mark(x1))), FIB1(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(fib1(0, x1)) -> c26(ACTIVE(fib1(active(0), mark(x1))), FIB1(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(fib1(cons(z0, z1), x1)) -> c26(ACTIVE(fib1(active(cons(mark(z0), z1)), mark(x1))), FIB1(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(fib1(add(z0, z1), x1)) -> c26(ACTIVE(fib1(active(add(mark(z0), mark(z1))), mark(x1))), FIB1(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) MARK(s(fib(z0))) -> c27(ACTIVE(s(active(fib(mark(z0))))), S(mark(fib(z0))), MARK(fib(z0))) MARK(s(sel(z0, z1))) -> c27(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(fib1(z0, z1))) -> c27(ACTIVE(s(active(fib1(mark(z0), mark(z1))))), S(mark(fib1(z0, z1))), MARK(fib1(z0, z1))) MARK(s(s(z0))) -> c27(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(0)) -> c27(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(cons(z0, z1))) -> c27(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(add(z0, z1))) -> c27(ACTIVE(s(active(add(mark(z0), mark(z1))))), S(mark(add(z0, z1))), MARK(add(z0, z1))) MARK(s(z0)) -> c27(S(mark(z0)), MARK(z0)) MARK(cons(fib(z0), x1)) -> c29(ACTIVE(cons(active(fib(mark(z0))), x1)), CONS(mark(fib(z0)), x1), MARK(fib(z0))) MARK(cons(sel(z0, z1), x1)) -> c29(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(fib1(z0, z1), x1)) -> c29(ACTIVE(cons(active(fib1(mark(z0), mark(z1))), x1)), CONS(mark(fib1(z0, z1)), x1), MARK(fib1(z0, z1))) MARK(cons(s(z0), x1)) -> c29(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(0, x1)) -> c29(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(cons(z0, z1), x1)) -> c29(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(add(z0, z1), x1)) -> c29(ACTIVE(cons(active(add(mark(z0), mark(z1))), x1)), CONS(mark(add(z0, z1)), x1), MARK(add(z0, z1))) MARK(cons(x0, x1)) -> c29(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c29(CONS(mark(z0), z1), MARK(z0)) MARK(add(z0, x1)) -> c30(ACTIVE(add(z0, mark(x1))), ADD(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(add(x0, z1)) -> c30(ACTIVE(add(mark(x0), z1)), ADD(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(add(x0, fib(z0))) -> c30(ACTIVE(add(mark(x0), active(fib(mark(z0))))), ADD(mark(x0), mark(fib(z0))), MARK(x0), MARK(fib(z0))) MARK(add(x0, sel(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(sel(mark(z0), mark(z1))))), ADD(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(add(x0, fib1(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(fib1(mark(z0), mark(z1))))), ADD(mark(x0), mark(fib1(z0, z1))), MARK(x0), MARK(fib1(z0, z1))) MARK(add(x0, s(z0))) -> c30(ACTIVE(add(mark(x0), active(s(mark(z0))))), ADD(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(add(x0, 0)) -> c30(ACTIVE(add(mark(x0), active(0))), ADD(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(add(x0, cons(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(cons(mark(z0), z1)))), ADD(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(add(x0, add(z0, z1))) -> c30(ACTIVE(add(mark(x0), active(add(mark(z0), mark(z1))))), ADD(mark(x0), mark(add(z0, z1))), MARK(x0), MARK(add(z0, z1))) MARK(add(fib(z0), x1)) -> c30(ACTIVE(add(active(fib(mark(z0))), mark(x1))), ADD(mark(fib(z0)), mark(x1)), MARK(fib(z0)), MARK(x1)) MARK(add(sel(z0, z1), x1)) -> c30(ACTIVE(add(active(sel(mark(z0), mark(z1))), mark(x1))), ADD(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(add(fib1(z0, z1), x1)) -> c30(ACTIVE(add(active(fib1(mark(z0), mark(z1))), mark(x1))), ADD(mark(fib1(z0, z1)), mark(x1)), MARK(fib1(z0, z1)), MARK(x1)) MARK(add(s(z0), x1)) -> c30(ACTIVE(add(active(s(mark(z0))), mark(x1))), ADD(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(add(0, x1)) -> c30(ACTIVE(add(active(0), mark(x1))), ADD(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c30(ACTIVE(add(active(cons(mark(z0), z1)), mark(x1))), ADD(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c30(ACTIVE(add(active(add(mark(z0), mark(z1))), mark(x1))), ADD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, fib_1, sel_2, fib1_2, s_1, cons_2, add_2 Defined Pair Symbols: ACTIVE_1, FIB_1, SEL_2, FIB1_2, S_1, CONS_2, ADD_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FIB_1, ENCODE_MARK_1, ENCODE_SEL_2, ENCODE_FIB1_2, ENCODE_S_1, ENCODE_CONS_2, ENCODE_ADD_2 Compound Symbols: c20_1, c22_1, c23_2, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c18_2, c19_2, c21_2, c28, c1_2, c2_2, c2_1, c3_2, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c8_3, c8_2, c24_3, c25_4, c26_4, c27_3, c27_2, c29_3, c29_1, c29_2, c30_4, c_1, c9_1, c10_1