/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 494 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 7156 ms] (14) BOUNDS(1, INF) (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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 1086 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms] (32) CpxRNTS (33) SimplificationProof [BOTH BOUNDS(ID, 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), 0 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), 54 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 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), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (64) CdtProblem (65) CdtLeafRemovalProof [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), 0 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtLeafRemovalProof [ComplexityIfPolyImplication, 14 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (162) CdtProblem (163) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 6 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) 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(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0, XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) 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(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_sel(x_1, x_2) -> sel(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(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0, XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_sel(x_1, x_2) -> sel(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(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0, XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) 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(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0, XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0', XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0', cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0') -> active(0') mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_nil -> nil encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: active(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0', XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0', cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0') -> active(0') mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) encArg(0') -> 0' encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_nil -> nil encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) Types: active :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel from :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel mark :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel s :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel head :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel 2nd :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel take :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel 0' :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel nil :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel sel :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encArg :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_active :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_mark :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_from :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_cons :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_s :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_head :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_2nd :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_take :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_sel :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_active :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_from :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_mark :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_cons :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_s :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_head :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_2nd :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_take :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_0 :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_nil :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_sel :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel hole_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel1_3 :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3 :: Nat -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: active, mark, cons, from, s, head, take, sel, 2nd, encArg They will be analysed ascendingly in the following order: active = mark cons < active from < active s < active head < active take < active sel < active active < encArg cons < mark from < mark s < mark head < mark take < mark sel < mark 2nd < mark mark < encArg cons < encArg from < encArg s < encArg head < encArg take < encArg sel < encArg 2nd < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: active(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0', XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0', cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0') -> active(0') mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) encArg(0') -> 0' encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_nil -> nil encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) Types: active :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel from :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel mark :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel s :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel head :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel 2nd :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel take :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel 0' :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel nil :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel sel :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encArg :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_active :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_mark :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_from :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_cons :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_s :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_head :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_2nd :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_take :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_sel :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_active :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_from :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_mark :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_cons :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_s :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_head :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_2nd :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_take :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_0 :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_nil :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_sel :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel hole_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel1_3 :: 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3 :: Nat -> 0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel Generator Equations: gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(0) <=> 0' gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(+(x, 1)) <=> cons_active(gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(x)) The following defined symbols remain to be analysed: cons, active, mark, from, s, head, take, sel, 2nd, encArg They will be analysed ascendingly in the following order: active = mark cons < active from < active s < active head < active take < active sel < active active < encArg cons < mark from < mark s < mark head < mark take < mark sel < mark 2nd < mark mark < encArg cons < encArg from < encArg s < encArg head < encArg take < encArg sel < encArg 2nd < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(+(1, n4146_3))) -> *3_3, rt in Omega(0) Induction Base: encArg(gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(+(1, 0))) Induction Step: encArg(gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(+(1, +(n4146_3, 1)))) ->_R^Omega(0) active(encArg(gen_0':nil:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel2_3(+(1, n4146_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). ---------------------------------------- (14) BOUNDS(1, INF) ---------------------------------------- (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(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, XS))) -> mark(X) active(2nd(cons(X, XS))) -> mark(head(XS)) active(take(0, XS)) -> mark(nil) active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(s(X)) -> active(s(mark(X))) mark(head(X)) -> active(head(mark(X))) mark(2nd(X)) -> active(2nd(mark(X))) mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) head(mark(X)) -> head(X) head(active(X)) -> head(X) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) take(mark(X1), X2) -> take(X1, X2) take(X1, mark(X2)) -> take(X1, X2) take(active(X1), X2) -> take(X1, X2) take(X1, active(X2)) -> take(X1, X2) 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) encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_sel(x_1, x_2) -> sel(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) mark(nil) -> active(nil) active(c_sel(0, c_cons(X, XS))) -> mark(X) mark(c_head(X)) -> active(head(mark(X))) from(c_mark(X)) -> from(X) active(c_head(c_cons(X, XS))) -> mark(X) take(X1, c_active(X2)) -> take(X1, X2) mark(c_s(X)) -> active(s(mark(X))) mark(c_from(X)) -> active(from(mark(X))) cons(c_mark(X1), X2) -> cons(X1, X2) s(c_active(X)) -> s(X) sel(c_active(X1), X2) -> sel(X1, X2) cons(X1, c_active(X2)) -> cons(X1, X2) head(c_active(X)) -> head(X) 2nd(c_mark(X)) -> 2nd(X) mark(c_take(X1, X2)) -> active(take(mark(X1), mark(X2))) cons(X1, c_mark(X2)) -> cons(X1, X2) take(c_mark(X1), X2) -> take(X1, X2) 2nd(c_active(X)) -> 2nd(X) active(c_2nd(c_cons(X, XS))) -> mark(head(XS)) from(c_active(X)) -> from(X) take(X1, c_mark(X2)) -> take(X1, X2) active(c_take(0, XS)) -> mark(nil) s(c_mark(X)) -> s(X) take(c_active(X1), X2) -> take(X1, X2) active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, take(N, XS))) mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) mark(c_2nd(X)) -> active(2nd(mark(X))) sel(c_mark(X1), X2) -> sel(X1, X2) head(c_mark(X)) -> head(X) cons(c_active(X1), X2) -> cons(X1, X2) mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) active(c_from(X)) -> mark(cons(X, from(s(X)))) 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(nil) -> nil encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) s(x0) -> c_s(x0) 2nd(x0) -> c_2nd(x0) active(x0) -> c_active(x0) take(x0, x1) -> c_take(x0, x1) head(x0) -> c_head(x0) cons(x0, x1) -> c_cons(x0, x1) sel(x0, x1) -> c_sel(x0, x1) from(x0) -> c_from(x0) 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] mark(nil) -> active(nil) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_head(X)) -> active(head(mark(X))) [1] from(c_mark(X)) -> from(X) [1] active(c_head(c_cons(X, XS))) -> mark(X) [1] take(X1, c_active(X2)) -> take(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_from(X)) -> active(from(mark(X))) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] s(c_active(X)) -> s(X) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] head(c_active(X)) -> head(X) [1] 2nd(c_mark(X)) -> 2nd(X) [1] mark(c_take(X1, X2)) -> active(take(mark(X1), mark(X2))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] take(c_mark(X1), X2) -> take(X1, X2) [1] 2nd(c_active(X)) -> 2nd(X) [1] active(c_2nd(c_cons(X, XS))) -> mark(head(XS)) [1] from(c_active(X)) -> from(X) [1] take(X1, c_mark(X2)) -> take(X1, X2) [1] active(c_take(0, XS)) -> mark(nil) [1] s(c_mark(X)) -> s(X) [1] take(c_active(X1), X2) -> take(X1, X2) [1] active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, take(N, XS))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] mark(c_2nd(X)) -> active(2nd(mark(X))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] head(c_mark(X)) -> head(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] active(c_from(X)) -> mark(cons(X, from(s(X)))) [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(nil) -> nil [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_from(x_1)) -> from(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_head(x_1)) -> head(encArg(x_1)) [0] encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) [0] encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_from(x_1) -> from(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_head(x_1) -> head(encArg(x_1)) [0] encode_2nd(x_1) -> 2nd(encArg(x_1)) [0] encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_nil -> nil [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] 2nd(x0) -> c_2nd(x0) [0] active(x0) -> c_active(x0) [0] take(x0, x1) -> c_take(x0, x1) [0] head(x0) -> c_head(x0) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] from(x0) -> c_from(x0) [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] mark(nil) -> active(nil) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_head(X)) -> active(head(mark(X))) [1] from(c_mark(X)) -> from(X) [1] active(c_head(c_cons(X, XS))) -> mark(X) [1] take(X1, c_active(X2)) -> take(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_from(X)) -> active(from(mark(X))) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] s(c_active(X)) -> s(X) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] head(c_active(X)) -> head(X) [1] 2nd(c_mark(X)) -> 2nd(X) [1] mark(c_take(X1, X2)) -> active(take(mark(X1), mark(X2))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] take(c_mark(X1), X2) -> take(X1, X2) [1] 2nd(c_active(X)) -> 2nd(X) [1] active(c_2nd(c_cons(X, XS))) -> mark(head(XS)) [1] from(c_active(X)) -> from(X) [1] take(X1, c_mark(X2)) -> take(X1, X2) [1] active(c_take(0, XS)) -> mark(nil) [1] s(c_mark(X)) -> s(X) [1] take(c_active(X1), X2) -> take(X1, X2) [1] active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, take(N, XS))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] mark(c_2nd(X)) -> active(2nd(mark(X))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] head(c_mark(X)) -> head(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] active(c_from(X)) -> mark(cons(X, from(s(X)))) [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(nil) -> nil [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_from(x_1)) -> from(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_head(x_1)) -> head(encArg(x_1)) [0] encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) [0] encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_from(x_1) -> from(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_head(x_1) -> head(encArg(x_1)) [0] encode_2nd(x_1) -> 2nd(encArg(x_1)) [0] encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_nil -> nil [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] 2nd(x0) -> c_2nd(x0) [0] active(x0) -> c_active(x0) [0] take(x0, x1) -> c_take(x0, x1) [0] head(x0) -> c_head(x0) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] from(x0) -> c_from(x0) [0] mark(x0) -> c_mark(x0) [0] The TRS has the following type information: mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel 0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel 2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel c_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encArg :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel cons_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel encode_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel Rewrite Strategy: INNERMOST ---------------------------------------- (23) 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_from(v0) -> null_encode_from [0] encode_mark(v0) -> null_encode_mark [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_s(v0) -> null_encode_s [0] encode_head(v0) -> null_encode_head [0] encode_2nd(v0) -> null_encode_2nd [0] encode_take(v0, v1) -> null_encode_take [0] encode_0 -> null_encode_0 [0] encode_nil -> null_encode_nil [0] encode_sel(v0, v1) -> null_encode_sel [0] s(v0) -> null_s [0] 2nd(v0) -> null_2nd [0] active(v0) -> null_active [0] take(v0, v1) -> null_take [0] head(v0) -> null_head [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] from(v0) -> null_from [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_from, null_encode_mark, null_encode_cons, null_encode_s, null_encode_head, null_encode_2nd, null_encode_take, null_encode_0, null_encode_nil, null_encode_sel, null_s, null_2nd, null_active, null_take, null_head, null_cons, null_sel, null_from, null_mark ---------------------------------------- (24) 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] mark(nil) -> active(nil) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_head(X)) -> active(head(mark(X))) [1] from(c_mark(X)) -> from(X) [1] active(c_head(c_cons(X, XS))) -> mark(X) [1] take(X1, c_active(X2)) -> take(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_from(X)) -> active(from(mark(X))) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] s(c_active(X)) -> s(X) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] head(c_active(X)) -> head(X) [1] 2nd(c_mark(X)) -> 2nd(X) [1] mark(c_take(X1, X2)) -> active(take(mark(X1), mark(X2))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] take(c_mark(X1), X2) -> take(X1, X2) [1] 2nd(c_active(X)) -> 2nd(X) [1] active(c_2nd(c_cons(X, XS))) -> mark(head(XS)) [1] from(c_active(X)) -> from(X) [1] take(X1, c_mark(X2)) -> take(X1, X2) [1] active(c_take(0, XS)) -> mark(nil) [1] s(c_mark(X)) -> s(X) [1] take(c_active(X1), X2) -> take(X1, X2) [1] active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, take(N, XS))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] mark(c_2nd(X)) -> active(2nd(mark(X))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] head(c_mark(X)) -> head(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] active(c_from(X)) -> mark(cons(X, from(s(X)))) [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(nil) -> nil [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_from(x_1)) -> from(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_head(x_1)) -> head(encArg(x_1)) [0] encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) [0] encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_from(x_1) -> from(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_head(x_1) -> head(encArg(x_1)) [0] encode_2nd(x_1) -> 2nd(encArg(x_1)) [0] encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_nil -> nil [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] 2nd(x0) -> c_2nd(x0) [0] active(x0) -> c_active(x0) [0] take(x0, x1) -> c_take(x0, x1) [0] head(x0) -> c_head(x0) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] from(x0) -> c_from(x0) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_from(v0) -> null_encode_from [0] encode_mark(v0) -> null_encode_mark [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_s(v0) -> null_encode_s [0] encode_head(v0) -> null_encode_head [0] encode_2nd(v0) -> null_encode_2nd [0] encode_take(v0, v1) -> null_encode_take [0] encode_0 -> null_encode_0 [0] encode_nil -> null_encode_nil [0] encode_sel(v0, v1) -> null_encode_sel [0] s(v0) -> null_s [0] 2nd(v0) -> null_2nd [0] active(v0) -> null_active [0] take(v0, v1) -> null_take [0] head(v0) -> null_head [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] from(v0) -> null_from [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark 0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark cons_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark cons_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encArg :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (25) 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 nil => 1 null_encArg => 0 null_encode_active => 0 null_encode_from => 0 null_encode_mark => 0 null_encode_cons => 0 null_encode_s => 0 null_encode_head => 0 null_encode_2nd => 0 null_encode_take => 0 null_encode_0 => 0 null_encode_nil => 0 null_encode_sel => 0 null_s => 0 null_2nd => 0 null_active => 0 null_take => 0 null_head => 0 null_cons => 0 null_sel => 0 null_from => 0 null_mark => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: 2nd(z) -{ 1 }-> 2nd(X) :|: z = 1 + X, X >= 0 2nd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 2nd(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 active(z) -{ 1 }-> mark(X) :|: X >= 0, XS >= 0, z = 1 + 0 + (1 + X + XS) active(z) -{ 1 }-> mark(X) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 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(head(XS)) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 1 }-> mark(cons(X, take(N, XS))) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(cons(X, from(s(X)))) :|: z = 1 + X, X >= 0 active(z) -{ 1 }-> mark(1) :|: z = 1 + 0 + XS, XS >= 0 active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 active(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 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 }-> take(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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(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 }-> head(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> from(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 }-> active(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 2nd(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_2nd(z) -{ 0 }-> 2nd(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_2nd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_active(z) -{ 0 }-> active(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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_from(z) -{ 0 }-> from(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_head(z) -{ 0 }-> head(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_head(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_mark(z) -{ 0 }-> mark(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_nil -{ 0 }-> 1 :|: encode_nil -{ 0 }-> 0 :|: 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 encode_take(z, z') -{ 0 }-> take(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 from(z) -{ 1 }-> from(X) :|: z = 1 + X, X >= 0 from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 from(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 head(z) -{ 1 }-> head(X) :|: z = 1 + X, X >= 0 head(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 head(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 mark(z) -{ 1 }-> active(take(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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(head(mark(X))) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(from(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(2nd(mark(X))) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(1) :|: z = 1 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 take(z, z') -{ 1 }-> take(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 take(z, z') -{ 1 }-> take(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 take(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (27) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_active_1 encode_from_1 encode_mark_1 encode_cons_2 encode_s_1 encode_head_1 encode_2nd_1 encode_take_2 encode_0 encode_nil encode_sel_2 s_1 2nd_1 active_1 take_2 head_1 cons_2 sel_2 from_1 mark_1 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_from(v0) -> null_encode_from [0] encode_mark(v0) -> null_encode_mark [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_s(v0) -> null_encode_s [0] encode_head(v0) -> null_encode_head [0] encode_2nd(v0) -> null_encode_2nd [0] encode_take(v0, v1) -> null_encode_take [0] encode_0 -> null_encode_0 [0] encode_nil -> null_encode_nil [0] encode_sel(v0, v1) -> null_encode_sel [0] s(v0) -> null_s [0] 2nd(v0) -> null_2nd [0] active(v0) -> null_active [0] take(v0, v1) -> null_take [0] head(v0) -> null_head [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] from(v0) -> null_from [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_from, null_encode_mark, null_encode_cons, null_encode_s, null_encode_head, null_encode_2nd, null_encode_take, null_encode_0, null_encode_nil, null_encode_sel, null_s, null_2nd, null_active, null_take, null_head, null_cons, null_sel, null_from, null_mark ---------------------------------------- (28) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(0) -> active(0) [1] mark(nil) -> active(nil) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_head(X)) -> active(head(mark(X))) [1] from(c_mark(X)) -> from(X) [1] active(c_head(c_cons(X, XS))) -> mark(X) [1] take(X1, c_active(X2)) -> take(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] mark(c_from(X)) -> active(from(mark(X))) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] s(c_active(X)) -> s(X) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] head(c_active(X)) -> head(X) [1] 2nd(c_mark(X)) -> 2nd(X) [1] mark(c_take(X1, X2)) -> active(take(mark(X1), mark(X2))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] take(c_mark(X1), X2) -> take(X1, X2) [1] 2nd(c_active(X)) -> 2nd(X) [1] active(c_2nd(c_cons(X, XS))) -> mark(head(XS)) [1] from(c_active(X)) -> from(X) [1] take(X1, c_mark(X2)) -> take(X1, X2) [1] active(c_take(0, XS)) -> mark(nil) [1] s(c_mark(X)) -> s(X) [1] take(c_active(X1), X2) -> take(X1, X2) [1] active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, take(N, XS))) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] mark(c_2nd(X)) -> active(2nd(mark(X))) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] head(c_mark(X)) -> head(X) [1] cons(c_active(X1), X2) -> cons(X1, X2) [1] mark(c_cons(X1, X2)) -> active(cons(mark(X1), X2)) [1] active(c_from(X)) -> mark(cons(X, from(s(X)))) [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(nil) -> nil [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_from(x_1)) -> from(encArg(x_1)) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_head(x_1)) -> head(encArg(x_1)) [0] encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) [0] encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_from(x_1) -> from(encArg(x_1)) [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_head(x_1) -> head(encArg(x_1)) [0] encode_2nd(x_1) -> 2nd(encArg(x_1)) [0] encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_nil -> nil [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] 2nd(x0) -> c_2nd(x0) [0] active(x0) -> c_active(x0) [0] take(x0, x1) -> c_take(x0, x1) [0] head(x0) -> c_head(x0) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] from(x0) -> c_from(x0) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_from(v0) -> null_encode_from [0] encode_mark(v0) -> null_encode_mark [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_s(v0) -> null_encode_s [0] encode_head(v0) -> null_encode_head [0] encode_2nd(v0) -> null_encode_2nd [0] encode_take(v0, v1) -> null_encode_take [0] encode_0 -> null_encode_0 [0] encode_nil -> null_encode_nil [0] encode_sel(v0, v1) -> null_encode_sel [0] s(v0) -> null_s [0] 2nd(v0) -> null_2nd [0] active(v0) -> null_active [0] take(v0, v1) -> null_take [0] head(v0) -> null_head [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] from(v0) -> null_from [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark 0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark c_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark c_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark c_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark head :: 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark cons_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark cons_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encArg :: 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_nil :: 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (29) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(0) -> active(0) [1] mark(nil) -> active(nil) [1] active(c_sel(0, c_cons(X, XS))) -> mark(X) [1] mark(c_head(0)) -> active(head(active(0))) [2] mark(c_head(nil)) -> active(head(active(nil))) [2] mark(c_head(c_head(X'))) -> active(head(active(head(mark(X'))))) [2] mark(c_head(c_s(X''))) -> active(head(active(s(mark(X''))))) [2] mark(c_head(c_from(X3))) -> active(head(active(from(mark(X3))))) [2] mark(c_head(c_take(X1', X2'))) -> active(head(active(take(mark(X1'), mark(X2'))))) [2] mark(c_head(c_sel(X1'', X2''))) -> active(head(active(sel(mark(X1''), mark(X2''))))) [2] mark(c_head(c_2nd(X4))) -> active(head(active(2nd(mark(X4))))) [2] mark(c_head(c_cons(X11, X21))) -> active(head(active(cons(mark(X11), X21)))) [2] mark(c_head(X)) -> active(head(c_mark(X))) [1] mark(c_head(X)) -> active(head(null_mark)) [1] from(c_mark(X)) -> from(X) [1] active(c_head(c_cons(X, XS))) -> mark(X) [1] take(X1, c_active(X2)) -> take(X1, X2) [1] mark(c_s(0)) -> active(s(active(0))) [2] mark(c_s(nil)) -> active(s(active(nil))) [2] mark(c_s(c_head(X5))) -> active(s(active(head(mark(X5))))) [2] mark(c_s(c_s(X6))) -> active(s(active(s(mark(X6))))) [2] mark(c_s(c_from(X7))) -> active(s(active(from(mark(X7))))) [2] mark(c_s(c_take(X12, X22))) -> active(s(active(take(mark(X12), mark(X22))))) [2] mark(c_s(c_sel(X13, X23))) -> active(s(active(sel(mark(X13), mark(X23))))) [2] mark(c_s(c_2nd(X8))) -> active(s(active(2nd(mark(X8))))) [2] mark(c_s(c_cons(X14, X24))) -> active(s(active(cons(mark(X14), X24)))) [2] mark(c_s(X)) -> active(s(c_mark(X))) [1] mark(c_s(X)) -> active(s(null_mark)) [1] mark(c_from(0)) -> active(from(active(0))) [2] mark(c_from(nil)) -> active(from(active(nil))) [2] mark(c_from(c_head(X9))) -> active(from(active(head(mark(X9))))) [2] mark(c_from(c_s(X10))) -> active(from(active(s(mark(X10))))) [2] mark(c_from(c_from(X15))) -> active(from(active(from(mark(X15))))) [2] mark(c_from(c_take(X16, X25))) -> active(from(active(take(mark(X16), mark(X25))))) [2] mark(c_from(c_sel(X17, X26))) -> active(from(active(sel(mark(X17), mark(X26))))) [2] mark(c_from(c_2nd(X18))) -> active(from(active(2nd(mark(X18))))) [2] mark(c_from(c_cons(X19, X27))) -> active(from(active(cons(mark(X19), X27)))) [2] mark(c_from(X)) -> active(from(c_mark(X))) [1] mark(c_from(X)) -> active(from(null_mark)) [1] cons(c_mark(X1), X2) -> cons(X1, X2) [1] s(c_active(X)) -> s(X) [1] sel(c_active(X1), X2) -> sel(X1, X2) [1] cons(X1, c_active(X2)) -> cons(X1, X2) [1] head(c_active(X)) -> head(X) [1] 2nd(c_mark(X)) -> 2nd(X) [1] mark(c_take(X1, X2)) -> active(take(mark(X1), mark(X2))) [1] cons(X1, c_mark(X2)) -> cons(X1, X2) [1] take(c_mark(X1), X2) -> take(X1, X2) [1] 2nd(c_active(X)) -> 2nd(X) [1] active(c_2nd(c_cons(X, c_active(X75)))) -> mark(head(X75)) [2] active(c_2nd(c_cons(X, c_mark(X76)))) -> mark(head(X76)) [2] active(c_2nd(c_cons(X, XS))) -> mark(c_head(XS)) [1] active(c_2nd(c_cons(X, XS))) -> mark(null_head) [1] from(c_active(X)) -> from(X) [1] take(X1, c_mark(X2)) -> take(X1, X2) [1] active(c_take(0, XS)) -> mark(nil) [1] s(c_mark(X)) -> s(X) [1] take(c_active(X1), X2) -> take(X1, X2) [1] active(c_take(c_s(N), c_cons(X, c_active(X246)))) -> mark(cons(X, take(N, X246))) [2] active(c_take(c_s(c_mark(X146)), c_cons(X, XS))) -> mark(cons(X, take(X146, XS))) [2] active(c_take(c_s(N), c_cons(X, c_mark(X247)))) -> mark(cons(X, take(N, X247))) [2] active(c_take(c_s(c_active(X147)), c_cons(X, XS))) -> mark(cons(X, take(X147, XS))) [2] active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, c_take(N, XS))) [1] active(c_take(c_s(N), c_cons(X, XS))) -> mark(cons(X, null_take)) [1] mark(c_sel(X1, X2)) -> active(sel(mark(X1), mark(X2))) [1] mark(c_2nd(0)) -> active(2nd(active(0))) [2] mark(c_2nd(nil)) -> active(2nd(active(nil))) [2] mark(c_2nd(c_head(X199))) -> active(2nd(active(head(mark(X199))))) [2] mark(c_2nd(c_s(X200))) -> active(2nd(active(s(mark(X200))))) [2] mark(c_2nd(c_from(X201))) -> active(2nd(active(from(mark(X201))))) [2] mark(c_2nd(c_take(X1100, X284))) -> active(2nd(active(take(mark(X1100), mark(X284))))) [2] mark(c_2nd(c_sel(X1101, X285))) -> active(2nd(active(sel(mark(X1101), mark(X285))))) [2] mark(c_2nd(c_2nd(X202))) -> active(2nd(active(2nd(mark(X202))))) [2] mark(c_2nd(c_cons(X1102, X286))) -> active(2nd(active(cons(mark(X1102), X286)))) [2] mark(c_2nd(X)) -> active(2nd(c_mark(X))) [1] mark(c_2nd(X)) -> active(2nd(null_mark)) [1] sel(c_mark(X1), X2) -> sel(X1, X2) [1] head(c_mark(X)) -> head(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(nil, X2)) -> active(cons(active(nil), X2)) [2] mark(c_cons(c_head(X203), X2)) -> active(cons(active(head(mark(X203))), X2)) [2] mark(c_cons(c_s(X204), X2)) -> active(cons(active(s(mark(X204))), X2)) [2] mark(c_cons(c_from(X205), X2)) -> active(cons(active(from(mark(X205))), X2)) [2] mark(c_cons(c_take(X1103, X287), X2)) -> active(cons(active(take(mark(X1103), mark(X287))), X2)) [2] mark(c_cons(c_sel(X1104, X288), X2)) -> active(cons(active(sel(mark(X1104), mark(X288))), X2)) [2] mark(c_cons(c_2nd(X206), X2)) -> active(cons(active(2nd(mark(X206))), X2)) [2] mark(c_cons(c_cons(X1105, X289), X2)) -> active(cons(active(cons(mark(X1105), X289)), X2)) [2] mark(c_cons(X1, X2)) -> active(cons(c_mark(X1), X2)) [1] mark(c_cons(X1, X2)) -> active(cons(null_mark, X2)) [1] active(c_from(c_active(X207))) -> mark(cons(c_active(X207), from(s(X207)))) [2] active(c_from(c_mark(X208))) -> mark(cons(c_mark(X208), from(s(X208)))) [2] active(c_from(X)) -> mark(cons(X, from(c_s(X)))) [1] active(c_from(X)) -> mark(cons(X, from(null_s))) [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(X1106)), c_cons(X, XS))) -> mark(sel(X1106, XS)) [2] active(c_sel(c_s(c_mark(X1107)), c_cons(X, XS))) -> mark(sel(X1107, XS)) [2] active(c_sel(c_s(N), c_cons(X, c_active(X290)))) -> mark(sel(N, X290)) [2] active(c_sel(c_s(N), c_cons(X, c_mark(X291)))) -> mark(sel(N, X291)) [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(null_sel) [1] encArg(0) -> 0 [0] encArg(nil) -> nil [0] encArg(cons_active(0)) -> active(0) [0] encArg(cons_active(nil)) -> active(nil) [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_from(x_11))) -> active(from(encArg(x_11))) [0] encArg(cons_active(cons_cons(x_12, x_2'))) -> active(cons(encArg(x_12), encArg(x_2'))) [0] encArg(cons_active(cons_s(x_13))) -> active(s(encArg(x_13))) [0] encArg(cons_active(cons_head(x_14))) -> active(head(encArg(x_14))) [0] encArg(cons_active(cons_2nd(x_15))) -> active(2nd(encArg(x_15))) [0] encArg(cons_active(cons_take(x_16, x_2''))) -> active(take(encArg(x_16), encArg(x_2''))) [0] encArg(cons_active(cons_sel(x_17, x_21))) -> active(sel(encArg(x_17), encArg(x_21))) [0] encArg(cons_active(x_1)) -> active(null_encArg) [0] encArg(cons_mark(0)) -> mark(0) [0] encArg(cons_mark(nil)) -> mark(nil) [0] encArg(cons_mark(cons_active(x_18))) -> mark(active(encArg(x_18))) [0] encArg(cons_mark(cons_mark(x_19))) -> mark(mark(encArg(x_19))) [0] encArg(cons_mark(cons_from(x_110))) -> mark(from(encArg(x_110))) [0] encArg(cons_mark(cons_cons(x_111, x_22))) -> mark(cons(encArg(x_111), encArg(x_22))) [0] encArg(cons_mark(cons_s(x_112))) -> mark(s(encArg(x_112))) [0] encArg(cons_mark(cons_head(x_113))) -> mark(head(encArg(x_113))) [0] encArg(cons_mark(cons_2nd(x_114))) -> mark(2nd(encArg(x_114))) [0] encArg(cons_mark(cons_take(x_115, x_23))) -> mark(take(encArg(x_115), encArg(x_23))) [0] encArg(cons_mark(cons_sel(x_116, x_24))) -> mark(sel(encArg(x_116), encArg(x_24))) [0] encArg(cons_mark(x_1)) -> mark(null_encArg) [0] encArg(cons_from(0)) -> from(0) [0] encArg(cons_from(nil)) -> from(nil) [0] encArg(cons_from(cons_active(x_117))) -> from(active(encArg(x_117))) [0] encArg(cons_from(cons_mark(x_118))) -> from(mark(encArg(x_118))) [0] encArg(cons_from(cons_from(x_119))) -> from(from(encArg(x_119))) [0] encArg(cons_from(cons_cons(x_120, x_25))) -> from(cons(encArg(x_120), encArg(x_25))) [0] encArg(cons_from(cons_s(x_121))) -> from(s(encArg(x_121))) [0] encArg(cons_from(cons_head(x_122))) -> from(head(encArg(x_122))) [0] encArg(cons_from(cons_2nd(x_123))) -> from(2nd(encArg(x_123))) [0] encArg(cons_from(cons_take(x_124, x_26))) -> from(take(encArg(x_124), encArg(x_26))) [0] encArg(cons_from(cons_sel(x_125, x_27))) -> from(sel(encArg(x_125), encArg(x_27))) [0] encArg(cons_from(x_1)) -> from(null_encArg) [0] encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(0)) -> s(0) [0] encArg(cons_s(nil)) -> s(nil) [0] encArg(cons_s(cons_active(x_1143))) -> s(active(encArg(x_1143))) [0] encArg(cons_s(cons_mark(x_1144))) -> s(mark(encArg(x_1144))) [0] encArg(cons_s(cons_from(x_1145))) -> s(from(encArg(x_1145))) [0] encArg(cons_s(cons_cons(x_1146, x_247))) -> s(cons(encArg(x_1146), encArg(x_247))) [0] encArg(cons_s(cons_s(x_1147))) -> s(s(encArg(x_1147))) [0] encArg(cons_s(cons_head(x_1148))) -> s(head(encArg(x_1148))) [0] encArg(cons_s(cons_2nd(x_1149))) -> s(2nd(encArg(x_1149))) [0] encArg(cons_s(cons_take(x_1150, x_248))) -> s(take(encArg(x_1150), encArg(x_248))) [0] encArg(cons_s(cons_sel(x_1151, x_249))) -> s(sel(encArg(x_1151), encArg(x_249))) [0] encArg(cons_s(x_1)) -> s(null_encArg) [0] encArg(cons_head(0)) -> head(0) [0] encArg(cons_head(nil)) -> head(nil) [0] encArg(cons_head(cons_active(x_1152))) -> head(active(encArg(x_1152))) [0] encArg(cons_head(cons_mark(x_1153))) -> head(mark(encArg(x_1153))) [0] encArg(cons_head(cons_from(x_1154))) -> head(from(encArg(x_1154))) [0] encArg(cons_head(cons_cons(x_1155, x_250))) -> head(cons(encArg(x_1155), encArg(x_250))) [0] encArg(cons_head(cons_s(x_1156))) -> head(s(encArg(x_1156))) [0] encArg(cons_head(cons_head(x_1157))) -> head(head(encArg(x_1157))) [0] encArg(cons_head(cons_2nd(x_1158))) -> head(2nd(encArg(x_1158))) [0] encArg(cons_head(cons_take(x_1159, x_251))) -> head(take(encArg(x_1159), encArg(x_251))) [0] encArg(cons_head(cons_sel(x_1160, x_252))) -> head(sel(encArg(x_1160), encArg(x_252))) [0] encArg(cons_head(x_1)) -> head(null_encArg) [0] encArg(cons_2nd(0)) -> 2nd(0) [0] encArg(cons_2nd(nil)) -> 2nd(nil) [0] encArg(cons_2nd(cons_active(x_1161))) -> 2nd(active(encArg(x_1161))) [0] encArg(cons_2nd(cons_mark(x_1162))) -> 2nd(mark(encArg(x_1162))) [0] encArg(cons_2nd(cons_from(x_1163))) -> 2nd(from(encArg(x_1163))) [0] encArg(cons_2nd(cons_cons(x_1164, x_253))) -> 2nd(cons(encArg(x_1164), encArg(x_253))) [0] encArg(cons_2nd(cons_s(x_1165))) -> 2nd(s(encArg(x_1165))) [0] encArg(cons_2nd(cons_head(x_1166))) -> 2nd(head(encArg(x_1166))) [0] encArg(cons_2nd(cons_2nd(x_1167))) -> 2nd(2nd(encArg(x_1167))) [0] encArg(cons_2nd(cons_take(x_1168, x_254))) -> 2nd(take(encArg(x_1168), encArg(x_254))) [0] encArg(cons_2nd(cons_sel(x_1169, x_255))) -> 2nd(sel(encArg(x_1169), encArg(x_255))) [0] encArg(cons_2nd(x_1)) -> 2nd(null_encArg) [0] encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) [0] encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) [0] encode_active(0) -> active(0) [0] encode_active(nil) -> active(nil) [0] encode_active(cons_active(x_1404)) -> active(active(encArg(x_1404))) [0] encode_active(cons_mark(x_1405)) -> active(mark(encArg(x_1405))) [0] encode_active(cons_from(x_1406)) -> active(from(encArg(x_1406))) [0] encode_active(cons_cons(x_1407, x_2134)) -> active(cons(encArg(x_1407), encArg(x_2134))) [0] encode_active(cons_s(x_1408)) -> active(s(encArg(x_1408))) [0] encode_active(cons_head(x_1409)) -> active(head(encArg(x_1409))) [0] encode_active(cons_2nd(x_1410)) -> active(2nd(encArg(x_1410))) [0] encode_active(cons_take(x_1411, x_2135)) -> active(take(encArg(x_1411), encArg(x_2135))) [0] encode_active(cons_sel(x_1412, x_2136)) -> active(sel(encArg(x_1412), encArg(x_2136))) [0] encode_active(x_1) -> active(null_encArg) [0] encode_from(0) -> from(0) [0] encode_from(nil) -> from(nil) [0] encode_from(cons_active(x_1413)) -> from(active(encArg(x_1413))) [0] encode_from(cons_mark(x_1414)) -> from(mark(encArg(x_1414))) [0] encode_from(cons_from(x_1415)) -> from(from(encArg(x_1415))) [0] encode_from(cons_cons(x_1416, x_2137)) -> from(cons(encArg(x_1416), encArg(x_2137))) [0] encode_from(cons_s(x_1417)) -> from(s(encArg(x_1417))) [0] encode_from(cons_head(x_1418)) -> from(head(encArg(x_1418))) [0] encode_from(cons_2nd(x_1419)) -> from(2nd(encArg(x_1419))) [0] encode_from(cons_take(x_1420, x_2138)) -> from(take(encArg(x_1420), encArg(x_2138))) [0] encode_from(cons_sel(x_1421, x_2139)) -> from(sel(encArg(x_1421), encArg(x_2139))) [0] encode_from(x_1) -> from(null_encArg) [0] encode_mark(0) -> mark(0) [0] encode_mark(nil) -> mark(nil) [0] encode_mark(cons_active(x_1422)) -> mark(active(encArg(x_1422))) [0] encode_mark(cons_mark(x_1423)) -> mark(mark(encArg(x_1423))) [0] encode_mark(cons_from(x_1424)) -> mark(from(encArg(x_1424))) [0] encode_mark(cons_cons(x_1425, x_2140)) -> mark(cons(encArg(x_1425), encArg(x_2140))) [0] encode_mark(cons_s(x_1426)) -> mark(s(encArg(x_1426))) [0] encode_mark(cons_head(x_1427)) -> mark(head(encArg(x_1427))) [0] encode_mark(cons_2nd(x_1428)) -> mark(2nd(encArg(x_1428))) [0] encode_mark(cons_take(x_1429, x_2141)) -> mark(take(encArg(x_1429), encArg(x_2141))) [0] encode_mark(cons_sel(x_1430, x_2142)) -> mark(sel(encArg(x_1430), encArg(x_2142))) [0] encode_mark(x_1) -> mark(null_encArg) [0] encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) [0] encode_s(0) -> s(0) [0] encode_s(nil) -> s(nil) [0] encode_s(cons_active(x_1548)) -> s(active(encArg(x_1548))) [0] encode_s(cons_mark(x_1549)) -> s(mark(encArg(x_1549))) [0] encode_s(cons_from(x_1550)) -> s(from(encArg(x_1550))) [0] encode_s(cons_cons(x_1551, x_2182)) -> s(cons(encArg(x_1551), encArg(x_2182))) [0] encode_s(cons_s(x_1552)) -> s(s(encArg(x_1552))) [0] encode_s(cons_head(x_1553)) -> s(head(encArg(x_1553))) [0] encode_s(cons_2nd(x_1554)) -> s(2nd(encArg(x_1554))) [0] encode_s(cons_take(x_1555, x_2183)) -> s(take(encArg(x_1555), encArg(x_2183))) [0] encode_s(cons_sel(x_1556, x_2184)) -> s(sel(encArg(x_1556), encArg(x_2184))) [0] encode_s(x_1) -> s(null_encArg) [0] encode_head(0) -> head(0) [0] encode_head(nil) -> head(nil) [0] encode_head(cons_active(x_1557)) -> head(active(encArg(x_1557))) [0] encode_head(cons_mark(x_1558)) -> head(mark(encArg(x_1558))) [0] encode_head(cons_from(x_1559)) -> head(from(encArg(x_1559))) [0] encode_head(cons_cons(x_1560, x_2185)) -> head(cons(encArg(x_1560), encArg(x_2185))) [0] encode_head(cons_s(x_1561)) -> head(s(encArg(x_1561))) [0] encode_head(cons_head(x_1562)) -> head(head(encArg(x_1562))) [0] encode_head(cons_2nd(x_1563)) -> head(2nd(encArg(x_1563))) [0] encode_head(cons_take(x_1564, x_2186)) -> head(take(encArg(x_1564), encArg(x_2186))) [0] encode_head(cons_sel(x_1565, x_2187)) -> head(sel(encArg(x_1565), encArg(x_2187))) [0] encode_head(x_1) -> head(null_encArg) [0] encode_2nd(0) -> 2nd(0) [0] encode_2nd(nil) -> 2nd(nil) [0] encode_2nd(cons_active(x_1566)) -> 2nd(active(encArg(x_1566))) [0] encode_2nd(cons_mark(x_1567)) -> 2nd(mark(encArg(x_1567))) [0] encode_2nd(cons_from(x_1568)) -> 2nd(from(encArg(x_1568))) [0] encode_2nd(cons_cons(x_1569, x_2188)) -> 2nd(cons(encArg(x_1569), encArg(x_2188))) [0] encode_2nd(cons_s(x_1570)) -> 2nd(s(encArg(x_1570))) [0] encode_2nd(cons_head(x_1571)) -> 2nd(head(encArg(x_1571))) [0] encode_2nd(cons_2nd(x_1572)) -> 2nd(2nd(encArg(x_1572))) [0] encode_2nd(cons_take(x_1573, x_2189)) -> 2nd(take(encArg(x_1573), encArg(x_2189))) [0] encode_2nd(cons_sel(x_1574, x_2190)) -> 2nd(sel(encArg(x_1574), encArg(x_2190))) [0] encode_2nd(x_1) -> 2nd(null_encArg) [0] encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_nil -> nil [0] encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] 2nd(x0) -> c_2nd(x0) [0] active(x0) -> c_active(x0) [0] take(x0, x1) -> c_take(x0, x1) [0] head(x0) -> c_head(x0) [0] cons(x0, x1) -> c_cons(x0, x1) [0] sel(x0, x1) -> c_sel(x0, x1) [0] from(x0) -> c_from(x0) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_from(v0) -> null_encode_from [0] encode_mark(v0) -> null_encode_mark [0] encode_cons(v0, v1) -> null_encode_cons [0] encode_s(v0) -> null_encode_s [0] encode_head(v0) -> null_encode_head [0] encode_2nd(v0) -> null_encode_2nd [0] encode_take(v0, v1) -> null_encode_take [0] encode_0 -> null_encode_0 [0] encode_nil -> null_encode_nil [0] encode_sel(v0, v1) -> null_encode_sel [0] s(v0) -> null_s [0] 2nd(v0) -> null_2nd [0] active(v0) -> null_active [0] take(v0, v1) -> null_take [0] head(v0) -> null_head [0] cons(v0, v1) -> null_cons [0] sel(v0, v1) -> null_sel [0] from(v0) -> null_from [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark 0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark c_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark c_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark cons_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 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0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark encode_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark -> 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encArg :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_0 :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_nil :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_encode_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_s :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_2nd :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_active :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_take :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_head :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_cons :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_sel :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_from :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark null_mark :: 0:nil:c_cons:c_sel:c_head:c_mark:c_active:c_s:c_from:c_take:c_2nd:cons_active:cons_mark:cons_from:cons_cons:cons_s:cons_head:cons_2nd:cons_take:cons_sel:null_encArg:null_encode_active:null_encode_from:null_encode_mark:null_encode_cons:null_encode_s:null_encode_head:null_encode_2nd:null_encode_take:null_encode_0:null_encode_nil:null_encode_sel:null_s:null_2nd:null_active:null_take:null_head:null_cons:null_sel:null_from:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 nil => 1 null_encArg => 0 null_encode_active => 0 null_encode_from => 0 null_encode_mark => 0 null_encode_cons => 0 null_encode_s => 0 null_encode_head => 0 null_encode_2nd => 0 null_encode_take => 0 null_encode_0 => 0 null_encode_nil => 0 null_encode_sel => 0 null_s => 0 null_2nd => 0 null_active => 0 null_take => 0 null_head => 0 null_cons => 0 null_sel => 0 null_from => 0 null_mark => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: 2nd(z) -{ 1 }-> 2nd(X) :|: z = 1 + X, X >= 0 2nd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 2nd(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 active(z) -{ 1 }-> mark(X) :|: X >= 0, XS >= 0, z = 1 + 0 + (1 + X + XS) active(z) -{ 1 }-> mark(X) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 2 }-> mark(sel(N, X290)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + (1 + X290)), X290 >= 0, N >= 0 active(z) -{ 2 }-> mark(sel(N, X291)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + (1 + X291)), X291 >= 0, N >= 0 active(z) -{ 2 }-> mark(sel(X1106, XS)) :|: X1106 >= 0, X >= 0, z = 1 + (1 + (1 + X1106)) + (1 + X + XS), XS >= 0 active(z) -{ 2 }-> mark(sel(X1107, XS)) :|: z = 1 + (1 + (1 + X1107)) + (1 + X + XS), X1107 >= 0, X >= 0, XS >= 0 active(z) -{ 2 }-> mark(head(X75)) :|: z = 1 + (1 + X + (1 + X75)), X75 >= 0, X >= 0 active(z) -{ 2 }-> mark(head(X76)) :|: z = 1 + (1 + X + (1 + X76)), X >= 0, X76 >= 0 active(z) -{ 2 }-> mark(cons(X, take(N, X246))) :|: z = 1 + (1 + N) + (1 + X + (1 + X246)), X >= 0, X246 >= 0, N >= 0 active(z) -{ 2 }-> mark(cons(X, take(N, X247))) :|: X >= 0, X247 >= 0, z = 1 + (1 + N) + (1 + X + (1 + X247)), N >= 0 active(z) -{ 2 }-> mark(cons(X, take(X146, XS))) :|: X146 >= 0, X >= 0, z = 1 + (1 + (1 + X146)) + (1 + X + XS), XS >= 0 active(z) -{ 2 }-> mark(cons(X, take(X147, XS))) :|: z = 1 + (1 + (1 + X147)) + (1 + X + XS), X147 >= 0, X >= 0, XS >= 0 active(z) -{ 1 }-> mark(cons(X, from(0))) :|: z = 1 + X, X >= 0 active(z) -{ 1 }-> mark(cons(X, from(1 + X))) :|: z = 1 + X, X >= 0 active(z) -{ 1 }-> mark(cons(X, 0)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(cons(X, 1 + N + XS)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 2 }-> mark(cons(1 + X207, from(s(X207)))) :|: z = 1 + (1 + X207), X207 >= 0 active(z) -{ 2 }-> mark(cons(1 + X208, from(s(X208)))) :|: z = 1 + (1 + X208), X208 >= 0 active(z) -{ 1 }-> mark(1) :|: z = 1 + 0 + XS, XS >= 0 active(z) -{ 1 }-> mark(0) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 1 }-> mark(0) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(1 + XS) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 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 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 }-> take(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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(take(encArg(x_1150), encArg(x_248))) :|: x_1150 >= 0, z = 1 + (1 + x_1150 + x_248), x_248 >= 0 encArg(z) -{ 0 }-> s(sel(encArg(x_1151), encArg(x_249))) :|: x_1151 >= 0, x_249 >= 0, z = 1 + (1 + x_1151 + x_249) encArg(z) -{ 0 }-> s(s(encArg(x_1147))) :|: x_1147 >= 0, z = 1 + (1 + x_1147) encArg(z) -{ 0 }-> s(mark(encArg(x_1144))) :|: z = 1 + (1 + x_1144), x_1144 >= 0 encArg(z) -{ 0 }-> s(head(encArg(x_1148))) :|: x_1148 >= 0, z = 1 + (1 + x_1148) encArg(z) -{ 0 }-> s(from(encArg(x_1145))) :|: x_1145 >= 0, z = 1 + (1 + x_1145) encArg(z) -{ 0 }-> s(cons(encArg(x_1146), encArg(x_247))) :|: x_1146 >= 0, x_247 >= 0, z = 1 + (1 + x_1146 + x_247) encArg(z) -{ 0 }-> s(active(encArg(x_1143))) :|: z = 1 + (1 + x_1143), x_1143 >= 0 encArg(z) -{ 0 }-> s(2nd(encArg(x_1149))) :|: z = 1 + (1 + x_1149), x_1149 >= 0 encArg(z) -{ 0 }-> s(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> s(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> s(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> mark(take(encArg(x_115), encArg(x_23))) :|: z = 1 + (1 + x_115 + x_23), x_115 >= 0, x_23 >= 0 encArg(z) -{ 0 }-> mark(sel(encArg(x_116), encArg(x_24))) :|: z = 1 + (1 + x_116 + x_24), x_116 >= 0, x_24 >= 0 encArg(z) -{ 0 }-> mark(s(encArg(x_112))) :|: x_112 >= 0, z = 1 + (1 + x_112) encArg(z) -{ 0 }-> mark(mark(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0 encArg(z) -{ 0 }-> mark(head(encArg(x_113))) :|: x_113 >= 0, z = 1 + (1 + x_113) encArg(z) -{ 0 }-> mark(from(encArg(x_110))) :|: z = 1 + (1 + x_110), x_110 >= 0 encArg(z) -{ 0 }-> mark(cons(encArg(x_111), encArg(x_22))) :|: z = 1 + (1 + x_111 + x_22), x_22 >= 0, x_111 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(x_18))) :|: z = 1 + (1 + x_18), x_18 >= 0 encArg(z) -{ 0 }-> mark(2nd(encArg(x_114))) :|: z = 1 + (1 + x_114), x_114 >= 0 encArg(z) -{ 0 }-> mark(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> head(take(encArg(x_1159), encArg(x_251))) :|: x_1159 >= 0, x_251 >= 0, z = 1 + (1 + x_1159 + x_251) encArg(z) -{ 0 }-> head(sel(encArg(x_1160), encArg(x_252))) :|: x_1160 >= 0, z = 1 + (1 + x_1160 + x_252), x_252 >= 0 encArg(z) -{ 0 }-> head(s(encArg(x_1156))) :|: x_1156 >= 0, z = 1 + (1 + x_1156) encArg(z) -{ 0 }-> head(mark(encArg(x_1153))) :|: z = 1 + (1 + x_1153), x_1153 >= 0 encArg(z) -{ 0 }-> head(head(encArg(x_1157))) :|: x_1157 >= 0, z = 1 + (1 + x_1157) encArg(z) -{ 0 }-> head(from(encArg(x_1154))) :|: x_1154 >= 0, z = 1 + (1 + x_1154) encArg(z) -{ 0 }-> head(cons(encArg(x_1155), encArg(x_250))) :|: x_250 >= 0, x_1155 >= 0, z = 1 + (1 + x_1155 + x_250) encArg(z) -{ 0 }-> head(active(encArg(x_1152))) :|: z = 1 + (1 + x_1152), x_1152 >= 0 encArg(z) -{ 0 }-> head(2nd(encArg(x_1158))) :|: x_1158 >= 0, z = 1 + (1 + x_1158) encArg(z) -{ 0 }-> head(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> head(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> head(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> from(take(encArg(x_124), encArg(x_26))) :|: z = 1 + (1 + x_124 + x_26), x_124 >= 0, x_26 >= 0 encArg(z) -{ 0 }-> from(sel(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, z = 1 + (1 + x_125 + x_27), x_27 >= 0 encArg(z) -{ 0 }-> from(s(encArg(x_121))) :|: z = 1 + (1 + x_121), x_121 >= 0 encArg(z) -{ 0 }-> from(mark(encArg(x_118))) :|: z = 1 + (1 + x_118), x_118 >= 0 encArg(z) -{ 0 }-> from(head(encArg(x_122))) :|: x_122 >= 0, z = 1 + (1 + x_122) encArg(z) -{ 0 }-> from(from(encArg(x_119))) :|: z = 1 + (1 + x_119), x_119 >= 0 encArg(z) -{ 0 }-> from(cons(encArg(x_120), encArg(x_25))) :|: x_120 >= 0, z = 1 + (1 + x_120 + x_25), x_25 >= 0 encArg(z) -{ 0 }-> from(active(encArg(x_117))) :|: z = 1 + (1 + x_117), x_117 >= 0 encArg(z) -{ 0 }-> from(2nd(encArg(x_123))) :|: x_123 >= 0, z = 1 + (1 + x_123) encArg(z) -{ 0 }-> from(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> from(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> from(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 }-> active(take(encArg(x_16), encArg(x_2''))) :|: x_16 >= 0, x_2'' >= 0, z = 1 + (1 + x_16 + x_2'') encArg(z) -{ 0 }-> active(sel(encArg(x_17), encArg(x_21))) :|: z = 1 + (1 + x_17 + x_21), x_17 >= 0, x_21 >= 0 encArg(z) -{ 0 }-> active(s(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> active(head(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14) encArg(z) -{ 0 }-> active(from(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11) encArg(z) -{ 0 }-> active(cons(encArg(x_12), encArg(x_2'))) :|: z = 1 + (1 + x_12 + x_2'), x_2' >= 0, x_12 >= 0 encArg(z) -{ 0 }-> active(active(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> active(2nd(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15) encArg(z) -{ 0 }-> active(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> active(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> active(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 2nd(take(encArg(x_1168), encArg(x_254))) :|: x_254 >= 0, x_1168 >= 0, z = 1 + (1 + x_1168 + x_254) encArg(z) -{ 0 }-> 2nd(sel(encArg(x_1169), encArg(x_255))) :|: x_1169 >= 0, x_255 >= 0, z = 1 + (1 + x_1169 + x_255) encArg(z) -{ 0 }-> 2nd(s(encArg(x_1165))) :|: x_1165 >= 0, z = 1 + (1 + x_1165) encArg(z) -{ 0 }-> 2nd(mark(encArg(x_1162))) :|: z = 1 + (1 + x_1162), x_1162 >= 0 encArg(z) -{ 0 }-> 2nd(head(encArg(x_1166))) :|: x_1166 >= 0, z = 1 + (1 + x_1166) encArg(z) -{ 0 }-> 2nd(from(encArg(x_1163))) :|: z = 1 + (1 + x_1163), x_1163 >= 0 encArg(z) -{ 0 }-> 2nd(cons(encArg(x_1164), encArg(x_253))) :|: x_253 >= 0, z = 1 + (1 + x_1164 + x_253), x_1164 >= 0 encArg(z) -{ 0 }-> 2nd(active(encArg(x_1161))) :|: z = 1 + (1 + x_1161), x_1161 >= 0 encArg(z) -{ 0 }-> 2nd(2nd(encArg(x_1167))) :|: x_1167 >= 0, z = 1 + (1 + x_1167) encArg(z) -{ 0 }-> 2nd(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> 2nd(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> 2nd(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_2nd(z) -{ 0 }-> 2nd(take(encArg(x_1573), encArg(x_2189))) :|: z = 1 + x_1573 + x_2189, x_1573 >= 0, x_2189 >= 0 encode_2nd(z) -{ 0 }-> 2nd(sel(encArg(x_1574), encArg(x_2190))) :|: x_2190 >= 0, x_1574 >= 0, z = 1 + x_1574 + x_2190 encode_2nd(z) -{ 0 }-> 2nd(s(encArg(x_1570))) :|: x_1570 >= 0, z = 1 + x_1570 encode_2nd(z) -{ 0 }-> 2nd(mark(encArg(x_1567))) :|: z = 1 + x_1567, x_1567 >= 0 encode_2nd(z) -{ 0 }-> 2nd(head(encArg(x_1571))) :|: z = 1 + x_1571, x_1571 >= 0 encode_2nd(z) -{ 0 }-> 2nd(from(encArg(x_1568))) :|: x_1568 >= 0, z = 1 + x_1568 encode_2nd(z) -{ 0 }-> 2nd(cons(encArg(x_1569), encArg(x_2188))) :|: z = 1 + x_1569 + x_2188, x_2188 >= 0, x_1569 >= 0 encode_2nd(z) -{ 0 }-> 2nd(active(encArg(x_1566))) :|: x_1566 >= 0, z = 1 + x_1566 encode_2nd(z) -{ 0 }-> 2nd(2nd(encArg(x_1572))) :|: z = 1 + x_1572, x_1572 >= 0 encode_2nd(z) -{ 0 }-> 2nd(1) :|: z = 1 encode_2nd(z) -{ 0 }-> 2nd(0) :|: z = 0 encode_2nd(z) -{ 0 }-> 2nd(0) :|: x_1 >= 0, z = x_1 encode_2nd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_active(z) -{ 0 }-> active(take(encArg(x_1411), encArg(x_2135))) :|: z = 1 + x_1411 + x_2135, x_2135 >= 0, x_1411 >= 0 encode_active(z) -{ 0 }-> active(sel(encArg(x_1412), encArg(x_2136))) :|: z = 1 + x_1412 + x_2136, x_1412 >= 0, x_2136 >= 0 encode_active(z) -{ 0 }-> active(s(encArg(x_1408))) :|: z = 1 + x_1408, x_1408 >= 0 encode_active(z) -{ 0 }-> active(mark(encArg(x_1405))) :|: x_1405 >= 0, z = 1 + x_1405 encode_active(z) -{ 0 }-> active(head(encArg(x_1409))) :|: z = 1 + x_1409, x_1409 >= 0 encode_active(z) -{ 0 }-> active(from(encArg(x_1406))) :|: x_1406 >= 0, z = 1 + x_1406 encode_active(z) -{ 0 }-> active(cons(encArg(x_1407), encArg(x_2134))) :|: x_2134 >= 0, z = 1 + x_1407 + x_2134, x_1407 >= 0 encode_active(z) -{ 0 }-> active(active(encArg(x_1404))) :|: x_1404 >= 0, z = 1 + x_1404 encode_active(z) -{ 0 }-> active(2nd(encArg(x_1410))) :|: z = 1 + x_1410, x_1410 >= 0 encode_active(z) -{ 0 }-> active(1) :|: z = 1 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_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_from(z) -{ 0 }-> from(take(encArg(x_1420), encArg(x_2138))) :|: z = 1 + x_1420 + x_2138, x_2138 >= 0, x_1420 >= 0 encode_from(z) -{ 0 }-> from(sel(encArg(x_1421), encArg(x_2139))) :|: x_2139 >= 0, z = 1 + x_1421 + x_2139, x_1421 >= 0 encode_from(z) -{ 0 }-> from(s(encArg(x_1417))) :|: z = 1 + x_1417, x_1417 >= 0 encode_from(z) -{ 0 }-> from(mark(encArg(x_1414))) :|: z = 1 + x_1414, x_1414 >= 0 encode_from(z) -{ 0 }-> from(head(encArg(x_1418))) :|: z = 1 + x_1418, x_1418 >= 0 encode_from(z) -{ 0 }-> from(from(encArg(x_1415))) :|: z = 1 + x_1415, x_1415 >= 0 encode_from(z) -{ 0 }-> from(cons(encArg(x_1416), encArg(x_2137))) :|: x_1416 >= 0, z = 1 + x_1416 + x_2137, x_2137 >= 0 encode_from(z) -{ 0 }-> from(active(encArg(x_1413))) :|: x_1413 >= 0, z = 1 + x_1413 encode_from(z) -{ 0 }-> from(2nd(encArg(x_1419))) :|: z = 1 + x_1419, x_1419 >= 0 encode_from(z) -{ 0 }-> from(1) :|: z = 1 encode_from(z) -{ 0 }-> from(0) :|: z = 0 encode_from(z) -{ 0 }-> from(0) :|: x_1 >= 0, z = x_1 encode_from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_head(z) -{ 0 }-> head(take(encArg(x_1564), encArg(x_2186))) :|: x_1564 >= 0, z = 1 + x_1564 + x_2186, x_2186 >= 0 encode_head(z) -{ 0 }-> head(sel(encArg(x_1565), encArg(x_2187))) :|: z = 1 + x_1565 + x_2187, x_2187 >= 0, x_1565 >= 0 encode_head(z) -{ 0 }-> head(s(encArg(x_1561))) :|: x_1561 >= 0, z = 1 + x_1561 encode_head(z) -{ 0 }-> head(mark(encArg(x_1558))) :|: x_1558 >= 0, z = 1 + x_1558 encode_head(z) -{ 0 }-> head(head(encArg(x_1562))) :|: x_1562 >= 0, z = 1 + x_1562 encode_head(z) -{ 0 }-> head(from(encArg(x_1559))) :|: x_1559 >= 0, z = 1 + x_1559 encode_head(z) -{ 0 }-> head(cons(encArg(x_1560), encArg(x_2185))) :|: x_1560 >= 0, x_2185 >= 0, z = 1 + x_1560 + x_2185 encode_head(z) -{ 0 }-> head(active(encArg(x_1557))) :|: x_1557 >= 0, z = 1 + x_1557 encode_head(z) -{ 0 }-> head(2nd(encArg(x_1563))) :|: x_1563 >= 0, z = 1 + x_1563 encode_head(z) -{ 0 }-> head(1) :|: z = 1 encode_head(z) -{ 0 }-> head(0) :|: z = 0 encode_head(z) -{ 0 }-> head(0) :|: x_1 >= 0, z = x_1 encode_head(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_mark(z) -{ 0 }-> mark(take(encArg(x_1429), encArg(x_2141))) :|: x_2141 >= 0, x_1429 >= 0, z = 1 + x_1429 + x_2141 encode_mark(z) -{ 0 }-> mark(sel(encArg(x_1430), encArg(x_2142))) :|: x_2142 >= 0, z = 1 + x_1430 + x_2142, x_1430 >= 0 encode_mark(z) -{ 0 }-> mark(s(encArg(x_1426))) :|: z = 1 + x_1426, x_1426 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(x_1423))) :|: x_1423 >= 0, z = 1 + x_1423 encode_mark(z) -{ 0 }-> mark(head(encArg(x_1427))) :|: x_1427 >= 0, z = 1 + x_1427 encode_mark(z) -{ 0 }-> mark(from(encArg(x_1424))) :|: z = 1 + x_1424, x_1424 >= 0 encode_mark(z) -{ 0 }-> mark(cons(encArg(x_1425), encArg(x_2140))) :|: x_1425 >= 0, x_2140 >= 0, z = 1 + x_1425 + x_2140 encode_mark(z) -{ 0 }-> mark(active(encArg(x_1422))) :|: z = 1 + x_1422, x_1422 >= 0 encode_mark(z) -{ 0 }-> mark(2nd(encArg(x_1428))) :|: z = 1 + x_1428, x_1428 >= 0 encode_mark(z) -{ 0 }-> mark(1) :|: z = 1 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_nil -{ 0 }-> 1 :|: encode_nil -{ 0 }-> 0 :|: encode_s(z) -{ 0 }-> s(take(encArg(x_1555), encArg(x_2183))) :|: z = 1 + x_1555 + x_2183, x_2183 >= 0, x_1555 >= 0 encode_s(z) -{ 0 }-> s(sel(encArg(x_1556), encArg(x_2184))) :|: x_2184 >= 0, z = 1 + x_1556 + x_2184, x_1556 >= 0 encode_s(z) -{ 0 }-> s(s(encArg(x_1552))) :|: z = 1 + x_1552, x_1552 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(x_1549))) :|: x_1549 >= 0, z = 1 + x_1549 encode_s(z) -{ 0 }-> s(head(encArg(x_1553))) :|: z = 1 + x_1553, x_1553 >= 0 encode_s(z) -{ 0 }-> s(from(encArg(x_1550))) :|: x_1550 >= 0, z = 1 + x_1550 encode_s(z) -{ 0 }-> s(cons(encArg(x_1551), encArg(x_2182))) :|: z = 1 + x_1551 + x_2182, x_2182 >= 0, x_1551 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(x_1548))) :|: z = 1 + x_1548, x_1548 >= 0 encode_s(z) -{ 0 }-> s(2nd(encArg(x_1554))) :|: x_1554 >= 0, z = 1 + x_1554 encode_s(z) -{ 0 }-> s(1) :|: z = 1 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 encode_take(z, z') -{ 0 }-> take(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 from(z) -{ 1 }-> from(X) :|: z = 1 + X, X >= 0 from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 from(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 head(z) -{ 1 }-> head(X) :|: z = 1 + X, X >= 0 head(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 head(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 mark(z) -{ 1 }-> active(take(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(sel(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(s(active(take(mark(X12), mark(X22))))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> active(s(active(sel(mark(X13), mark(X23))))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(X6))))) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> active(s(active(head(mark(X5))))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> active(s(active(from(mark(X7))))) :|: X7 >= 0, z = 1 + (1 + X7) mark(z) -{ 2 }-> active(s(active(cons(mark(X14), X24)))) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> active(s(active(2nd(mark(X8))))) :|: X8 >= 0, z = 1 + (1 + X8) mark(z) -{ 2 }-> active(s(active(1))) :|: z = 1 + 1 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) -{ 2 }-> active(head(active(take(mark(X1'), mark(X2'))))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 mark(z) -{ 2 }-> active(head(active(sel(mark(X1''), mark(X2''))))) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 mark(z) -{ 2 }-> active(head(active(s(mark(X''))))) :|: z = 1 + (1 + X''), X'' >= 0 mark(z) -{ 2 }-> active(head(active(head(mark(X'))))) :|: X' >= 0, z = 1 + (1 + X') mark(z) -{ 2 }-> active(head(active(from(mark(X3))))) :|: z = 1 + (1 + X3), X3 >= 0 mark(z) -{ 2 }-> active(head(active(cons(mark(X11), X21)))) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 mark(z) -{ 2 }-> active(head(active(2nd(mark(X4))))) :|: z = 1 + (1 + X4), X4 >= 0 mark(z) -{ 2 }-> active(head(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(head(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(head(0)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(head(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> active(from(active(take(mark(X16), mark(X25))))) :|: X16 >= 0, z = 1 + (1 + X16 + X25), X25 >= 0 mark(z) -{ 2 }-> active(from(active(sel(mark(X17), mark(X26))))) :|: z = 1 + (1 + X17 + X26), X26 >= 0, X17 >= 0 mark(z) -{ 2 }-> active(from(active(s(mark(X10))))) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> active(from(active(head(mark(X9))))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> active(from(active(from(mark(X15))))) :|: z = 1 + (1 + X15), X15 >= 0 mark(z) -{ 2 }-> active(from(active(cons(mark(X19), X27)))) :|: z = 1 + (1 + X19 + X27), X19 >= 0, X27 >= 0 mark(z) -{ 2 }-> active(from(active(2nd(mark(X18))))) :|: X18 >= 0, z = 1 + (1 + X18) mark(z) -{ 2 }-> active(from(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(from(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(from(0)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(from(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> active(cons(active(take(mark(X1103), mark(X287))), X2)) :|: z = 1 + (1 + X1103 + X287) + X2, X287 >= 0, X2 >= 0, X1103 >= 0 mark(z) -{ 2 }-> active(cons(active(sel(mark(X1104), mark(X288))), X2)) :|: X1104 >= 0, X288 >= 0, z = 1 + (1 + X1104 + X288) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(s(mark(X204))), X2)) :|: X204 >= 0, z = 1 + (1 + X204) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(head(mark(X203))), X2)) :|: X203 >= 0, X2 >= 0, z = 1 + (1 + X203) + X2 mark(z) -{ 2 }-> active(cons(active(from(mark(X205))), X2)) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(cons(mark(X1105), X289)), X2)) :|: X1105 >= 0, z = 1 + (1 + X1105 + X289) + X2, X289 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(2nd(mark(X206))), X2)) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(1), X2)) :|: z = 1 + 1 + X2, X2 >= 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) -{ 2 }-> active(2nd(active(take(mark(X1100), mark(X284))))) :|: X1100 >= 0, X284 >= 0, z = 1 + (1 + X1100 + X284) mark(z) -{ 2 }-> active(2nd(active(sel(mark(X1101), mark(X285))))) :|: X1101 >= 0, z = 1 + (1 + X1101 + X285), X285 >= 0 mark(z) -{ 2 }-> active(2nd(active(s(mark(X200))))) :|: z = 1 + (1 + X200), X200 >= 0 mark(z) -{ 2 }-> active(2nd(active(head(mark(X199))))) :|: z = 1 + (1 + X199), X199 >= 0 mark(z) -{ 2 }-> active(2nd(active(from(mark(X201))))) :|: X201 >= 0, z = 1 + (1 + X201) mark(z) -{ 2 }-> active(2nd(active(cons(mark(X1102), X286)))) :|: X286 >= 0, z = 1 + (1 + X1102 + X286), X1102 >= 0 mark(z) -{ 2 }-> active(2nd(active(2nd(mark(X202))))) :|: X202 >= 0, z = 1 + (1 + X202) mark(z) -{ 2 }-> active(2nd(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(2nd(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(2nd(0)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(2nd(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(1) :|: z = 1 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 take(z, z') -{ 1 }-> take(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 take(z, z') -{ 1 }-> take(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 take(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 ---------------------------------------- (33) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: 2nd(z) -{ 1 }-> 2nd(z - 1) :|: z - 1 >= 0 2nd(z) -{ 0 }-> 0 :|: z >= 0 2nd(z) -{ 0 }-> 1 + z :|: z >= 0 active(z) -{ 1 }-> mark(X) :|: X >= 0, XS >= 0, z = 1 + 0 + (1 + X + XS) active(z) -{ 1 }-> mark(X) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 2 }-> mark(sel(N, X290)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + (1 + X290)), X290 >= 0, N >= 0 active(z) -{ 2 }-> mark(sel(N, X291)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + (1 + X291)), X291 >= 0, N >= 0 active(z) -{ 2 }-> mark(sel(X1106, XS)) :|: X1106 >= 0, X >= 0, z = 1 + (1 + (1 + X1106)) + (1 + X + XS), XS >= 0 active(z) -{ 2 }-> mark(sel(X1107, XS)) :|: z = 1 + (1 + (1 + X1107)) + (1 + X + XS), X1107 >= 0, X >= 0, XS >= 0 active(z) -{ 2 }-> mark(head(X75)) :|: z = 1 + (1 + X + (1 + X75)), X75 >= 0, X >= 0 active(z) -{ 2 }-> mark(head(X76)) :|: z = 1 + (1 + X + (1 + X76)), X >= 0, X76 >= 0 active(z) -{ 2 }-> mark(cons(X, take(N, X246))) :|: z = 1 + (1 + N) + (1 + X + (1 + X246)), X >= 0, X246 >= 0, N >= 0 active(z) -{ 2 }-> mark(cons(X, take(N, X247))) :|: X >= 0, X247 >= 0, z = 1 + (1 + N) + (1 + X + (1 + X247)), N >= 0 active(z) -{ 2 }-> mark(cons(X, take(X146, XS))) :|: X146 >= 0, X >= 0, z = 1 + (1 + (1 + X146)) + (1 + X + XS), XS >= 0 active(z) -{ 2 }-> mark(cons(X, take(X147, XS))) :|: z = 1 + (1 + (1 + X147)) + (1 + X + XS), X147 >= 0, X >= 0, XS >= 0 active(z) -{ 1 }-> mark(cons(X, 0)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(cons(X, 1 + N + XS)) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(cons(z - 1, from(0))) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(cons(z - 1, from(1 + (z - 1)))) :|: z - 1 >= 0 active(z) -{ 2 }-> mark(cons(1 + (z - 2), from(s(z - 2)))) :|: z - 2 >= 0 active(z) -{ 1 }-> mark(1) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(0) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 0 active(z) -{ 1 }-> mark(0) :|: X >= 0, z = 1 + (1 + N) + (1 + X + XS), XS >= 0, N >= 0 active(z) -{ 1 }-> mark(1 + XS) :|: z = 1 + (1 + X + XS), X >= 0, XS >= 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 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 }-> take(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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(take(encArg(x_1150), encArg(x_248))) :|: x_1150 >= 0, z = 1 + (1 + x_1150 + x_248), x_248 >= 0 encArg(z) -{ 0 }-> s(sel(encArg(x_1151), encArg(x_249))) :|: x_1151 >= 0, x_249 >= 0, z = 1 + (1 + x_1151 + x_249) 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(head(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(from(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(cons(encArg(x_1146), encArg(x_247))) :|: x_1146 >= 0, x_247 >= 0, z = 1 + (1 + x_1146 + x_247) encArg(z) -{ 0 }-> s(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(2nd(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> s(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> s(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> mark(take(encArg(x_115), encArg(x_23))) :|: z = 1 + (1 + x_115 + x_23), x_115 >= 0, x_23 >= 0 encArg(z) -{ 0 }-> mark(sel(encArg(x_116), encArg(x_24))) :|: z = 1 + (1 + x_116 + x_24), x_116 >= 0, x_24 >= 0 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(head(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(from(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(cons(encArg(x_111), encArg(x_22))) :|: z = 1 + (1 + x_111 + x_22), x_22 >= 0, x_111 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(2nd(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> head(take(encArg(x_1159), encArg(x_251))) :|: x_1159 >= 0, x_251 >= 0, z = 1 + (1 + x_1159 + x_251) encArg(z) -{ 0 }-> head(sel(encArg(x_1160), encArg(x_252))) :|: x_1160 >= 0, z = 1 + (1 + x_1160 + x_252), x_252 >= 0 encArg(z) -{ 0 }-> head(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> head(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> head(head(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> head(from(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> head(cons(encArg(x_1155), encArg(x_250))) :|: x_250 >= 0, x_1155 >= 0, z = 1 + (1 + x_1155 + x_250) encArg(z) -{ 0 }-> head(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> head(2nd(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> head(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> head(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> head(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> from(take(encArg(x_124), encArg(x_26))) :|: z = 1 + (1 + x_124 + x_26), x_124 >= 0, x_26 >= 0 encArg(z) -{ 0 }-> from(sel(encArg(x_125), encArg(x_27))) :|: x_125 >= 0, z = 1 + (1 + x_125 + x_27), x_27 >= 0 encArg(z) -{ 0 }-> from(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> from(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> from(head(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> from(from(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> from(cons(encArg(x_120), encArg(x_25))) :|: x_120 >= 0, z = 1 + (1 + x_120 + x_25), x_25 >= 0 encArg(z) -{ 0 }-> from(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> from(2nd(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> from(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> from(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> from(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 }-> active(take(encArg(x_16), encArg(x_2''))) :|: x_16 >= 0, x_2'' >= 0, z = 1 + (1 + x_16 + x_2'') encArg(z) -{ 0 }-> active(sel(encArg(x_17), encArg(x_21))) :|: z = 1 + (1 + x_17 + x_21), x_17 >= 0, x_21 >= 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(head(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(from(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(cons(encArg(x_12), encArg(x_2'))) :|: z = 1 + (1 + x_12 + x_2'), x_2' >= 0, x_12 >= 0 encArg(z) -{ 0 }-> active(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(2nd(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> active(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> active(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 2nd(take(encArg(x_1168), encArg(x_254))) :|: x_254 >= 0, x_1168 >= 0, z = 1 + (1 + x_1168 + x_254) encArg(z) -{ 0 }-> 2nd(sel(encArg(x_1169), encArg(x_255))) :|: x_1169 >= 0, x_255 >= 0, z = 1 + (1 + x_1169 + x_255) encArg(z) -{ 0 }-> 2nd(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2nd(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2nd(head(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2nd(from(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2nd(cons(encArg(x_1164), encArg(x_253))) :|: x_253 >= 0, z = 1 + (1 + x_1164 + x_253), x_1164 >= 0 encArg(z) -{ 0 }-> 2nd(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2nd(2nd(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2nd(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> 2nd(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> 2nd(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_0 -{ 0 }-> 0 :|: encode_2nd(z) -{ 0 }-> 2nd(take(encArg(x_1573), encArg(x_2189))) :|: z = 1 + x_1573 + x_2189, x_1573 >= 0, x_2189 >= 0 encode_2nd(z) -{ 0 }-> 2nd(sel(encArg(x_1574), encArg(x_2190))) :|: x_2190 >= 0, x_1574 >= 0, z = 1 + x_1574 + x_2190 encode_2nd(z) -{ 0 }-> 2nd(s(encArg(z - 1))) :|: z - 1 >= 0 encode_2nd(z) -{ 0 }-> 2nd(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_2nd(z) -{ 0 }-> 2nd(head(encArg(z - 1))) :|: z - 1 >= 0 encode_2nd(z) -{ 0 }-> 2nd(from(encArg(z - 1))) :|: z - 1 >= 0 encode_2nd(z) -{ 0 }-> 2nd(cons(encArg(x_1569), encArg(x_2188))) :|: z = 1 + x_1569 + x_2188, x_2188 >= 0, x_1569 >= 0 encode_2nd(z) -{ 0 }-> 2nd(active(encArg(z - 1))) :|: z - 1 >= 0 encode_2nd(z) -{ 0 }-> 2nd(2nd(encArg(z - 1))) :|: z - 1 >= 0 encode_2nd(z) -{ 0 }-> 2nd(1) :|: z = 1 encode_2nd(z) -{ 0 }-> 2nd(0) :|: z = 0 encode_2nd(z) -{ 0 }-> 2nd(0) :|: z >= 0 encode_2nd(z) -{ 0 }-> 0 :|: z >= 0 encode_active(z) -{ 0 }-> active(take(encArg(x_1411), encArg(x_2135))) :|: z = 1 + x_1411 + x_2135, x_2135 >= 0, x_1411 >= 0 encode_active(z) -{ 0 }-> active(sel(encArg(x_1412), encArg(x_2136))) :|: z = 1 + x_1412 + x_2136, x_1412 >= 0, x_2136 >= 0 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(head(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(from(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(cons(encArg(x_1407), encArg(x_2134))) :|: x_2134 >= 0, z = 1 + x_1407 + x_2134, x_1407 >= 0 encode_active(z) -{ 0 }-> active(active(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(2nd(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(1) :|: z = 1 encode_active(z) -{ 0 }-> active(0) :|: z = 0 encode_active(z) -{ 0 }-> active(0) :|: z >= 0 encode_active(z) -{ 0 }-> 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_from(z) -{ 0 }-> from(take(encArg(x_1420), encArg(x_2138))) :|: z = 1 + x_1420 + x_2138, x_2138 >= 0, x_1420 >= 0 encode_from(z) -{ 0 }-> from(sel(encArg(x_1421), encArg(x_2139))) :|: x_2139 >= 0, z = 1 + x_1421 + x_2139, x_1421 >= 0 encode_from(z) -{ 0 }-> from(s(encArg(z - 1))) :|: z - 1 >= 0 encode_from(z) -{ 0 }-> from(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_from(z) -{ 0 }-> from(head(encArg(z - 1))) :|: z - 1 >= 0 encode_from(z) -{ 0 }-> from(from(encArg(z - 1))) :|: z - 1 >= 0 encode_from(z) -{ 0 }-> from(cons(encArg(x_1416), encArg(x_2137))) :|: x_1416 >= 0, z = 1 + x_1416 + x_2137, x_2137 >= 0 encode_from(z) -{ 0 }-> from(active(encArg(z - 1))) :|: z - 1 >= 0 encode_from(z) -{ 0 }-> from(2nd(encArg(z - 1))) :|: z - 1 >= 0 encode_from(z) -{ 0 }-> from(1) :|: z = 1 encode_from(z) -{ 0 }-> from(0) :|: z = 0 encode_from(z) -{ 0 }-> from(0) :|: z >= 0 encode_from(z) -{ 0 }-> 0 :|: z >= 0 encode_head(z) -{ 0 }-> head(take(encArg(x_1564), encArg(x_2186))) :|: x_1564 >= 0, z = 1 + x_1564 + x_2186, x_2186 >= 0 encode_head(z) -{ 0 }-> head(sel(encArg(x_1565), encArg(x_2187))) :|: z = 1 + x_1565 + x_2187, x_2187 >= 0, x_1565 >= 0 encode_head(z) -{ 0 }-> head(s(encArg(z - 1))) :|: z - 1 >= 0 encode_head(z) -{ 0 }-> head(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_head(z) -{ 0 }-> head(head(encArg(z - 1))) :|: z - 1 >= 0 encode_head(z) -{ 0 }-> head(from(encArg(z - 1))) :|: z - 1 >= 0 encode_head(z) -{ 0 }-> head(cons(encArg(x_1560), encArg(x_2185))) :|: x_1560 >= 0, x_2185 >= 0, z = 1 + x_1560 + x_2185 encode_head(z) -{ 0 }-> head(active(encArg(z - 1))) :|: z - 1 >= 0 encode_head(z) -{ 0 }-> head(2nd(encArg(z - 1))) :|: z - 1 >= 0 encode_head(z) -{ 0 }-> head(1) :|: z = 1 encode_head(z) -{ 0 }-> head(0) :|: z = 0 encode_head(z) -{ 0 }-> head(0) :|: z >= 0 encode_head(z) -{ 0 }-> 0 :|: z >= 0 encode_mark(z) -{ 0 }-> mark(take(encArg(x_1429), encArg(x_2141))) :|: x_2141 >= 0, x_1429 >= 0, z = 1 + x_1429 + x_2141 encode_mark(z) -{ 0 }-> mark(sel(encArg(x_1430), encArg(x_2142))) :|: x_2142 >= 0, z = 1 + x_1430 + x_2142, x_1430 >= 0 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(head(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(from(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(cons(encArg(x_1425), encArg(x_2140))) :|: x_1425 >= 0, x_2140 >= 0, z = 1 + x_1425 + x_2140 encode_mark(z) -{ 0 }-> mark(active(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(2nd(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(1) :|: z = 1 encode_mark(z) -{ 0 }-> mark(0) :|: z = 0 encode_mark(z) -{ 0 }-> mark(0) :|: z >= 0 encode_mark(z) -{ 0 }-> 0 :|: z >= 0 encode_nil -{ 0 }-> 1 :|: encode_nil -{ 0 }-> 0 :|: encode_s(z) -{ 0 }-> s(take(encArg(x_1555), encArg(x_2183))) :|: z = 1 + x_1555 + x_2183, x_2183 >= 0, x_1555 >= 0 encode_s(z) -{ 0 }-> s(sel(encArg(x_1556), encArg(x_2184))) :|: x_2184 >= 0, z = 1 + x_1556 + x_2184, x_1556 >= 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(head(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(from(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(cons(encArg(x_1551), encArg(x_2182))) :|: z = 1 + x_1551 + x_2182, x_2182 >= 0, x_1551 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(2nd(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(1) :|: z = 1 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 encode_take(z, z') -{ 0 }-> take(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_take(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 from(z) -{ 1 }-> from(z - 1) :|: z - 1 >= 0 from(z) -{ 0 }-> 0 :|: z >= 0 from(z) -{ 0 }-> 1 + z :|: z >= 0 head(z) -{ 1 }-> head(z - 1) :|: z - 1 >= 0 head(z) -{ 0 }-> 0 :|: z >= 0 head(z) -{ 0 }-> 1 + z :|: z >= 0 mark(z) -{ 1 }-> active(take(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(sel(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(s(active(take(mark(X12), mark(X22))))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> active(s(active(sel(mark(X13), mark(X23))))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(head(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(from(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(cons(mark(X14), X24)))) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> active(s(active(2nd(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(1))) :|: z = 1 + 1 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) -{ 2 }-> active(head(active(take(mark(X1'), mark(X2'))))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 mark(z) -{ 2 }-> active(head(active(sel(mark(X1''), mark(X2''))))) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 mark(z) -{ 2 }-> active(head(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(head(active(head(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(head(active(from(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(head(active(cons(mark(X11), X21)))) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 mark(z) -{ 2 }-> active(head(active(2nd(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(head(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(head(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(head(0)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(head(1 + (z - 1))) :|: z - 1 >= 0 mark(z) -{ 2 }-> active(from(active(take(mark(X16), mark(X25))))) :|: X16 >= 0, z = 1 + (1 + X16 + X25), X25 >= 0 mark(z) -{ 2 }-> active(from(active(sel(mark(X17), mark(X26))))) :|: z = 1 + (1 + X17 + X26), X26 >= 0, X17 >= 0 mark(z) -{ 2 }-> active(from(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(from(active(head(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(from(active(from(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(from(active(cons(mark(X19), X27)))) :|: z = 1 + (1 + X19 + X27), X19 >= 0, X27 >= 0 mark(z) -{ 2 }-> active(from(active(2nd(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(from(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(from(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(from(0)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(from(1 + (z - 1))) :|: z - 1 >= 0 mark(z) -{ 2 }-> active(cons(active(take(mark(X1103), mark(X287))), X2)) :|: z = 1 + (1 + X1103 + X287) + X2, X287 >= 0, X2 >= 0, X1103 >= 0 mark(z) -{ 2 }-> active(cons(active(sel(mark(X1104), mark(X288))), X2)) :|: X1104 >= 0, X288 >= 0, z = 1 + (1 + X1104 + X288) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(s(mark(X204))), X2)) :|: X204 >= 0, z = 1 + (1 + X204) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(head(mark(X203))), X2)) :|: X203 >= 0, X2 >= 0, z = 1 + (1 + X203) + X2 mark(z) -{ 2 }-> active(cons(active(from(mark(X205))), X2)) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(cons(mark(X1105), X289)), X2)) :|: X1105 >= 0, z = 1 + (1 + X1105 + X289) + X2, X289 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(2nd(mark(X206))), X2)) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> active(cons(active(1), z - 2)) :|: z - 2 >= 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) -{ 2 }-> active(2nd(active(take(mark(X1100), mark(X284))))) :|: X1100 >= 0, X284 >= 0, z = 1 + (1 + X1100 + X284) mark(z) -{ 2 }-> active(2nd(active(sel(mark(X1101), mark(X285))))) :|: X1101 >= 0, z = 1 + (1 + X1101 + X285), X285 >= 0 mark(z) -{ 2 }-> active(2nd(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(2nd(active(head(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(2nd(active(from(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(2nd(active(cons(mark(X1102), X286)))) :|: X286 >= 0, z = 1 + (1 + X1102 + X286), X1102 >= 0 mark(z) -{ 2 }-> active(2nd(active(2nd(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(2nd(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(2nd(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(2nd(0)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(2nd(1 + (z - 1))) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(1) :|: z = 1 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 take(z, z') -{ 1 }-> take(z, z' - 1) :|: z >= 0, z' - 1 >= 0 take(z, z') -{ 1 }-> take(z - 1, z') :|: z - 1 >= 0, z' >= 0 take(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 take(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_from(z0) -> from(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_head(z0) -> head(encArg(z0)) encode_2nd(z0) -> 2nd(encArg(z0)) encode_take(z0, z1) -> take(encArg(z0), encArg(z1)) encode_0 -> 0 encode_nil -> nil encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(0) -> c ENCARG(nil) -> c1 ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c11(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_FROM(z0) -> c12(FROM(encArg(z0)), ENCARG(z0)) ENCODE_MARK(z0) -> c13(MARK(encArg(z0)), ENCARG(z0)) ENCODE_CONS(z0, z1) -> c14(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c15(S(encArg(z0)), ENCARG(z0)) ENCODE_HEAD(z0) -> c16(HEAD(encArg(z0)), ENCARG(z0)) ENCODE_2ND(z0) -> c17(2ND(encArg(z0)), ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c18(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_0 -> c19 ENCODE_NIL -> c20 ENCODE_SEL(z0, z1) -> c21(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c35(ACTIVE(0)) MARK(nil) -> c36(ACTIVE(nil)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) S tuples: ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c35(ACTIVE(0)) MARK(nil) -> c36(ACTIVE(nil)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2, encArg_1, encode_active_1, encode_from_1, encode_mark_1, encode_cons_2, encode_s_1, encode_head_1, encode_2nd_1, encode_take_2, encode_0, encode_nil, encode_sel_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_0, ENCODE_NIL, ENCODE_SEL_2, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2 Compound Symbols: c, c1, c2_2, c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c11_2, c12_2, c13_2, c14_3, c15_2, c16_2, c17_2, c18_3, c19, c20, c21_3, c22_4, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c35_1, c36_1, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: ENCODE_NIL -> c20 ENCODE_0 -> c19 ENCARG(nil) -> c1 ENCARG(0) -> c ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_from(z0) -> from(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_head(z0) -> head(encArg(z0)) encode_2nd(z0) -> 2nd(encArg(z0)) encode_take(z0, z1) -> take(encArg(z0), encArg(z1)) encode_0 -> 0 encode_nil -> nil encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c11(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_FROM(z0) -> c12(FROM(encArg(z0)), ENCARG(z0)) ENCODE_MARK(z0) -> c13(MARK(encArg(z0)), ENCARG(z0)) ENCODE_CONS(z0, z1) -> c14(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c15(S(encArg(z0)), ENCARG(z0)) ENCODE_HEAD(z0) -> c16(HEAD(encArg(z0)), ENCARG(z0)) ENCODE_2ND(z0) -> c17(2ND(encArg(z0)), ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c18(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_SEL(z0, z1) -> c21(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c35(ACTIVE(0)) MARK(nil) -> c36(ACTIVE(nil)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) S tuples: ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c35(ACTIVE(0)) MARK(nil) -> c36(ACTIVE(nil)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2, encArg_1, encode_active_1, encode_from_1, encode_mark_1, encode_cons_2, encode_s_1, encode_head_1, encode_2nd_1, encode_take_2, encode_0, encode_nil, encode_sel_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2 Compound Symbols: c2_2, c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c11_2, c12_2, c13_2, c14_3, c15_2, c16_2, c17_2, c18_3, c21_3, c22_4, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c35_1, c36_1, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_from(z0) -> from(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_head(z0) -> head(encArg(z0)) encode_2nd(z0) -> 2nd(encArg(z0)) encode_take(z0, z1) -> take(encArg(z0), encArg(z1)) encode_0 -> 0 encode_nil -> nil encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c11(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_FROM(z0) -> c12(FROM(encArg(z0)), ENCARG(z0)) ENCODE_MARK(z0) -> c13(MARK(encArg(z0)), ENCARG(z0)) ENCODE_CONS(z0, z1) -> c14(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c15(S(encArg(z0)), ENCARG(z0)) ENCODE_HEAD(z0) -> c16(HEAD(encArg(z0)), ENCARG(z0)) ENCODE_2ND(z0) -> c17(2ND(encArg(z0)), ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c18(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_SEL(z0, z1) -> c21(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2, encArg_1, encode_active_1, encode_from_1, encode_mark_1, encode_cons_2, encode_s_1, encode_head_1, encode_2nd_1, encode_take_2, encode_0, encode_nil, encode_sel_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2 Compound Symbols: c2_2, c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c11_2, c12_2, c13_2, c14_3, c15_2, c16_2, c17_2, c18_3, c21_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36 ---------------------------------------- (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(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_from(z0) -> from(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_head(z0) -> head(encArg(z0)) encode_2nd(z0) -> 2nd(encArg(z0)) encode_take(z0, z1) -> take(encArg(z0), encArg(z1)) encode_0 -> 0 encode_nil -> nil encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_FROM(z0) -> c(ENCARG(z0)) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_MARK(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_S(z0) -> c(S(encArg(z0))) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_HEAD(z0) -> c(ENCARG(z0)) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_2ND(z0) -> c(ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_TAKE(z0, z1) -> c(ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c(ENCARG(z1)) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(ENCARG(z0)) ENCODE_SEL(z0, z1) -> c(ENCARG(z1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2, encArg_1, encode_active_1, encode_from_1, encode_mark_1, encode_cons_2, encode_s_1, encode_head_1, encode_2nd_1, encode_take_2, encode_0, encode_nil, encode_sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c2_2, c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 12 leading nodes: ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_FROM(z0) -> c(ENCARG(z0)) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_CONS(z0, z1) -> c(ENCARG(z0)) ENCODE_CONS(z0, z1) -> c(ENCARG(z1)) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_HEAD(z0) -> c(ENCARG(z0)) ENCODE_2ND(z0) -> c(ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c(ENCARG(z0)) ENCODE_TAKE(z0, z1) -> c(ENCARG(z1)) ENCODE_SEL(z0, z1) -> c(ENCARG(z0)) ENCODE_SEL(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_from(z0) -> from(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_head(z0) -> head(encArg(z0)) encode_2nd(z0) -> 2nd(encArg(z0)) encode_take(z0, z1) -> take(encArg(z0), encArg(z1)) encode_0 -> 0 encode_nil -> nil encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2, encArg_1, encode_active_1, encode_from_1, encode_mark_1, encode_cons_2, encode_s_1, encode_head_1, encode_2nd_1, encode_take_2, encode_0, encode_nil, encode_sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c2_2, c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_active(z0) -> active(encArg(z0)) encode_from(z0) -> from(encArg(z0)) encode_mark(z0) -> mark(encArg(z0)) encode_cons(z0, z1) -> cons(encArg(z0), encArg(z1)) encode_s(z0) -> s(encArg(z0)) encode_head(z0) -> head(encArg(z0)) encode_2nd(z0) -> 2nd(encArg(z0)) encode_take(z0, z1) -> take(encArg(z0), encArg(z1)) encode_0 -> 0 encode_nil -> nil encode_sel(z0, z1) -> sel(encArg(z0), encArg(z1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c2_2, c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) by ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(nil)) -> c2(ACTIVE(nil), ENCARG(nil)) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(nil)) -> c2(ACTIVE(nil), ENCARG(nil)) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(nil)) -> c2(ACTIVE(nil), ENCARG(nil)) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c3_2, c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) by ENCARG(cons_mark(0)) -> c3(MARK(0), ENCARG(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil), ENCARG(nil)) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0), ENCARG(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil), ENCARG(nil)) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c4_2, c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_from(z0)) -> c4(FROM(encArg(z0)), ENCARG(z0)) by ENCARG(cons_from(0)) -> c4(FROM(0), ENCARG(0)) ENCARG(cons_from(nil)) -> c4(FROM(nil), ENCARG(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(0)) -> c4(FROM(0), ENCARG(0)) ENCARG(cons_from(nil)) -> c4(FROM(nil), ENCARG(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_from(nil)) -> c4(FROM(nil), ENCARG(nil)) ENCARG(cons_from(0)) -> c4(FROM(0), ENCARG(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c5_3, c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_cons(z0, z1)) -> c5(CONS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c6_2, c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2 ---------------------------------------- (63) 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(nil)) -> c6(S(nil), ENCARG(nil)) 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(nil)) -> c6(S(nil), ENCARG(nil)) 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_s(nil)) -> c6(S(nil), ENCARG(nil)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c7_2, c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_head(z0)) -> c7(HEAD(encArg(z0)), ENCARG(z0)) by ENCARG(cons_head(0)) -> c7(HEAD(0), ENCARG(0)) ENCARG(cons_head(nil)) -> c7(HEAD(nil), ENCARG(nil)) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(0)) -> c7(HEAD(0), ENCARG(0)) ENCARG(cons_head(nil)) -> c7(HEAD(nil), ENCARG(nil)) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_head(0)) -> c7(HEAD(0), ENCARG(0)) ENCARG(cons_head(nil)) -> c7(HEAD(nil), ENCARG(nil)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c8_2, c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_2nd(z0)) -> c8(2ND(encArg(z0)), ENCARG(z0)) by ENCARG(cons_2nd(0)) -> c8(2ND(0), ENCARG(0)) ENCARG(cons_2nd(nil)) -> c8(2ND(nil), ENCARG(nil)) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(0)) -> c8(2ND(0), ENCARG(0)) ENCARG(cons_2nd(nil)) -> c8(2ND(nil), ENCARG(nil)) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_2nd(0)) -> c8(2ND(0), ENCARG(0)) ENCARG(cons_2nd(nil)) -> c8(2ND(nil), ENCARG(nil)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c9_3, c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_take(z0, z1)) -> c9(TAKE(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c10_3, c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_sel(z0, z1)) -> c10(SEL(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c29_3, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(from(z0)) -> c29(ACTIVE(from(mark(z0))), FROM(mark(z0)), MARK(z0)) by MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c30_3, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(cons(z0, z1)) -> c30(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0)) by MARK(cons(z0, z1)) -> c30(ACTIVE(cons(z0, z1)), CONS(mark(z0), z1), MARK(z0)) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(z0, z1)), CONS(mark(z0), z1), MARK(z0)) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(z0, z1)) -> c30(ACTIVE(cons(z0, z1)), CONS(mark(z0), z1), MARK(z0)) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c31_3, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) by MARK(s(z0)) -> c31(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c32_3, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(head(z0)) -> c32(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0)) by MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c33_3, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(2nd(z0)) -> c33(ACTIVE(2nd(mark(z0))), 2ND(mark(z0)), MARK(z0)) by MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c34_4, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c34(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, MARK_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, c37_4, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(z0, z1)) -> c37(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (101) 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(nil) -> c(ACTIVE(nil)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(nil) -> c(ACTIVE(nil)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ACTIVE(nil) -> c(ACTIVE(nil)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_FROM(z0) -> c(FROM(encArg(z0))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_FROM(z0) -> c(FROM(encArg(z0))) by ENCODE_FROM(0) -> c(FROM(0)) ENCODE_FROM(nil) -> c(FROM(nil)) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(encArg(z0), encArg(z1)))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(0) -> c(FROM(0)) ENCODE_FROM(nil) -> c(FROM(nil)) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_FROM(nil) -> c(FROM(nil)) ENCODE_FROM(0) -> c(FROM(0)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (109) 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(nil) -> c(MARK(nil)) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(encArg(z0), encArg(z1)))) ENCODE_MARK(0) -> c(MARK(0)) ENCODE_MARK(nil) -> c(MARK(nil)) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (111) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_MARK(0) -> c(MARK(0)) ENCODE_MARK(nil) -> c(MARK(nil)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_CONS(z0, z1) -> c(CONS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (113) 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, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (115) 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(nil) -> c(S(nil)) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(0) -> c(S(0)) ENCODE_S(nil) -> c(S(nil)) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_S(nil) -> c(S(nil)) ENCODE_S(0) -> c(S(0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_HEAD(z0) -> c(HEAD(encArg(z0))) by ENCODE_HEAD(0) -> c(HEAD(0)) ENCODE_HEAD(nil) -> c(HEAD(nil)) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(0) -> c(HEAD(0)) ENCODE_HEAD(nil) -> c(HEAD(nil)) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_HEAD(nil) -> c(HEAD(nil)) ENCODE_HEAD(0) -> c(HEAD(0)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_2ND(z0) -> c(2ND(encArg(z0))) ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_2ND(z0) -> c(2ND(encArg(z0))) by ENCODE_2ND(0) -> c(2ND(0)) ENCODE_2ND(nil) -> c(2ND(nil)) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(0) -> c(2ND(0)) ENCODE_2ND(nil) -> c(2ND(nil)) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_2ND(nil) -> c(2ND(nil)) ENCODE_2ND(0) -> c(2ND(0)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_TAKE_2, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_TAKE(z0, z1) -> c(TAKE(encArg(z0), encArg(z1))) by ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCODE_SEL(z0, z1) -> c(SEL(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCODE_SEL_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c_1, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4 ---------------------------------------- (129) 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, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) by ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) ENCARG(cons_active(cons_active(nil))) -> c2(ACTIVE(active(nil)), ENCARG(cons_active(nil))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) ENCARG(cons_active(cons_active(nil))) -> c2(ACTIVE(active(nil)), ENCARG(cons_active(nil))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) ENCARG(cons_active(cons_active(nil))) -> c2(ACTIVE(active(nil)), ENCARG(cons_active(nil))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) by ENCARG(cons_active(cons_mark(0))) -> c2(ACTIVE(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c2(ACTIVE(mark(nil)), ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c2(ACTIVE(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c2(ACTIVE(mark(nil)), ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1 ---------------------------------------- (137) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_cons(z0, z1))) -> c2(ACTIVE(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) by ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) by ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(nil))) -> c2(ACTIVE(s(nil)), ENCARG(cons_s(nil))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(nil))) -> c2(ACTIVE(s(nil)), ENCARG(cons_s(nil))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(nil))) -> c2(ACTIVE(s(nil)), ENCARG(cons_s(nil))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_head(z0))) -> c2(ACTIVE(head(encArg(z0))), ENCARG(cons_head(z0))) by ENCARG(cons_active(cons_head(0))) -> c2(ACTIVE(head(0)), ENCARG(cons_head(0))) ENCARG(cons_active(cons_head(nil))) -> c2(ACTIVE(head(nil)), ENCARG(cons_head(nil))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(0))) -> c2(ACTIVE(head(0)), ENCARG(cons_head(0))) ENCARG(cons_active(cons_head(nil))) -> c2(ACTIVE(head(nil)), ENCARG(cons_head(nil))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_head(nil))) -> c2(ACTIVE(head(nil)), ENCARG(cons_head(nil))) ENCARG(cons_active(cons_head(0))) -> c2(ACTIVE(head(0)), ENCARG(cons_head(0))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_2nd(z0))) -> c2(ACTIVE(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) by ENCARG(cons_active(cons_2nd(0))) -> c2(ACTIVE(2nd(0)), ENCARG(cons_2nd(0))) ENCARG(cons_active(cons_2nd(nil))) -> c2(ACTIVE(2nd(nil)), ENCARG(cons_2nd(nil))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(0))) -> c2(ACTIVE(2nd(0)), ENCARG(cons_2nd(0))) ENCARG(cons_active(cons_2nd(nil))) -> c2(ACTIVE(2nd(nil)), ENCARG(cons_2nd(nil))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_2nd(nil))) -> c2(ACTIVE(2nd(nil)), ENCARG(cons_2nd(nil))) ENCARG(cons_active(cons_2nd(0))) -> c2(ACTIVE(2nd(0)), ENCARG(cons_2nd(0))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_take(z0, z1))) -> c2(ACTIVE(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) by ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_sel(z0, z1))) -> c2(ACTIVE(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) by ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) by ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) ENCARG(cons_mark(cons_active(nil))) -> c3(MARK(active(nil)), ENCARG(cons_active(nil))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) ENCARG(cons_mark(cons_active(nil))) -> c3(MARK(active(nil)), ENCARG(cons_active(nil))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_mark(cons_active(nil))) -> c3(MARK(active(nil)), ENCARG(cons_active(nil))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) by ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c3(MARK(mark(nil)), ENCARG(cons_mark(nil))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c3(MARK(mark(nil)), ENCARG(cons_mark(nil))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1 ---------------------------------------- (163) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c11(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c11(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c11(MARK(mark(nil))) ENCARG(cons_mark(cons_mark(nil))) -> c11(ENCARG(cons_mark(nil))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1, c11_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_from(cons_from(z0))) -> c4(FROM(from(encArg(z0))), ENCARG(cons_from(z0))) by ENCARG(cons_from(cons_from(0))) -> c4(FROM(from(0)), ENCARG(cons_from(0))) ENCARG(cons_from(cons_from(nil))) -> c4(FROM(from(nil)), ENCARG(cons_from(nil))) ENCARG(cons_from(cons_from(cons_active(z0)))) -> c4(FROM(from(active(encArg(z0)))), ENCARG(cons_from(cons_active(z0)))) ENCARG(cons_from(cons_from(cons_mark(z0)))) -> c4(FROM(from(mark(encArg(z0)))), ENCARG(cons_from(cons_mark(z0)))) ENCARG(cons_from(cons_from(cons_from(z0)))) -> c4(FROM(from(from(encArg(z0)))), ENCARG(cons_from(cons_from(z0)))) ENCARG(cons_from(cons_from(cons_cons(z0, z1)))) -> c4(FROM(from(cons(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_cons(z0, z1)))) ENCARG(cons_from(cons_from(cons_s(z0)))) -> c4(FROM(from(s(encArg(z0)))), ENCARG(cons_from(cons_s(z0)))) ENCARG(cons_from(cons_from(cons_head(z0)))) -> c4(FROM(from(head(encArg(z0)))), ENCARG(cons_from(cons_head(z0)))) ENCARG(cons_from(cons_from(cons_2nd(z0)))) -> c4(FROM(from(2nd(encArg(z0)))), ENCARG(cons_from(cons_2nd(z0)))) ENCARG(cons_from(cons_from(cons_take(z0, z1)))) -> c4(FROM(from(take(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_take(z0, z1)))) ENCARG(cons_from(cons_from(cons_sel(z0, z1)))) -> c4(FROM(from(sel(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_sel(z0, z1)))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c11(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c11(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c11(MARK(mark(nil))) ENCARG(cons_mark(cons_mark(nil))) -> c11(ENCARG(cons_mark(nil))) ENCARG(cons_from(cons_from(0))) -> c4(FROM(from(0)), ENCARG(cons_from(0))) ENCARG(cons_from(cons_from(nil))) -> c4(FROM(from(nil)), ENCARG(cons_from(nil))) ENCARG(cons_from(cons_from(cons_active(z0)))) -> c4(FROM(from(active(encArg(z0)))), ENCARG(cons_from(cons_active(z0)))) ENCARG(cons_from(cons_from(cons_mark(z0)))) -> c4(FROM(from(mark(encArg(z0)))), ENCARG(cons_from(cons_mark(z0)))) ENCARG(cons_from(cons_from(cons_from(z0)))) -> c4(FROM(from(from(encArg(z0)))), ENCARG(cons_from(cons_from(z0)))) ENCARG(cons_from(cons_from(cons_cons(z0, z1)))) -> c4(FROM(from(cons(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_cons(z0, z1)))) ENCARG(cons_from(cons_from(cons_s(z0)))) -> c4(FROM(from(s(encArg(z0)))), ENCARG(cons_from(cons_s(z0)))) ENCARG(cons_from(cons_from(cons_head(z0)))) -> c4(FROM(from(head(encArg(z0)))), ENCARG(cons_from(cons_head(z0)))) ENCARG(cons_from(cons_from(cons_2nd(z0)))) -> c4(FROM(from(2nd(encArg(z0)))), ENCARG(cons_from(cons_2nd(z0)))) ENCARG(cons_from(cons_from(cons_take(z0, z1)))) -> c4(FROM(from(take(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_take(z0, z1)))) ENCARG(cons_from(cons_from(cons_sel(z0, z1)))) -> c4(FROM(from(sel(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1, c11_1 ---------------------------------------- (167) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_from(cons_from(nil))) -> c4(FROM(from(nil)), ENCARG(cons_from(nil))) ENCARG(cons_from(cons_from(0))) -> c4(FROM(from(0)), ENCARG(cons_from(0))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c11(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c11(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c11(MARK(mark(nil))) ENCARG(cons_mark(cons_mark(nil))) -> c11(ENCARG(cons_mark(nil))) ENCARG(cons_from(cons_from(cons_active(z0)))) -> c4(FROM(from(active(encArg(z0)))), ENCARG(cons_from(cons_active(z0)))) ENCARG(cons_from(cons_from(cons_mark(z0)))) -> c4(FROM(from(mark(encArg(z0)))), ENCARG(cons_from(cons_mark(z0)))) ENCARG(cons_from(cons_from(cons_from(z0)))) -> c4(FROM(from(from(encArg(z0)))), ENCARG(cons_from(cons_from(z0)))) ENCARG(cons_from(cons_from(cons_cons(z0, z1)))) -> c4(FROM(from(cons(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_cons(z0, z1)))) ENCARG(cons_from(cons_from(cons_s(z0)))) -> c4(FROM(from(s(encArg(z0)))), ENCARG(cons_from(cons_s(z0)))) ENCARG(cons_from(cons_from(cons_head(z0)))) -> c4(FROM(from(head(encArg(z0)))), ENCARG(cons_from(cons_head(z0)))) ENCARG(cons_from(cons_from(cons_2nd(z0)))) -> c4(FROM(from(2nd(encArg(z0)))), ENCARG(cons_from(cons_2nd(z0)))) ENCARG(cons_from(cons_from(cons_take(z0, z1)))) -> c4(FROM(from(take(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_take(z0, z1)))) ENCARG(cons_from(cons_from(cons_sel(z0, z1)))) -> c4(FROM(from(sel(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1, c11_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_from(cons_cons(z0, z1))) -> c4(FROM(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) by ENCARG(cons_from(cons_cons(x0, 0))) -> c4(FROM(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_from(cons_cons(x0, nil))) -> c4(FROM(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_from(cons_cons(x0, cons_active(z0)))) -> c4(FROM(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_from(cons_cons(x0, cons_mark(z0)))) -> c4(FROM(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_from(cons_cons(x0, cons_from(z0)))) -> c4(FROM(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_from(cons_cons(x0, cons_cons(z0, z1)))) -> c4(FROM(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_s(z0)))) -> c4(FROM(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_from(cons_cons(x0, cons_head(z0)))) -> c4(FROM(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_from(cons_cons(x0, cons_2nd(z0)))) -> c4(FROM(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_from(cons_cons(x0, cons_take(z0, z1)))) -> c4(FROM(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_sel(z0, z1)))) -> c4(FROM(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(0, x1))) -> c4(FROM(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_from(cons_cons(nil, x1))) -> c4(FROM(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_from(cons_cons(cons_active(z0), x1))) -> c4(FROM(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_from(cons_cons(cons_mark(z0), x1))) -> c4(FROM(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_from(cons_cons(cons_from(z0), x1))) -> c4(FROM(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_from(cons_cons(cons_cons(z0, z1), x1))) -> c4(FROM(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_s(z0), x1))) -> c4(FROM(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_from(cons_cons(cons_head(z0), x1))) -> c4(FROM(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_from(cons_cons(cons_2nd(z0), x1))) -> c4(FROM(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_from(cons_cons(cons_take(z0, z1), x1))) -> c4(FROM(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_sel(z0, z1), x1))) -> c4(FROM(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c11(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c11(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c11(MARK(mark(nil))) ENCARG(cons_mark(cons_mark(nil))) -> c11(ENCARG(cons_mark(nil))) ENCARG(cons_from(cons_from(cons_active(z0)))) -> c4(FROM(from(active(encArg(z0)))), ENCARG(cons_from(cons_active(z0)))) ENCARG(cons_from(cons_from(cons_mark(z0)))) -> c4(FROM(from(mark(encArg(z0)))), ENCARG(cons_from(cons_mark(z0)))) ENCARG(cons_from(cons_from(cons_from(z0)))) -> c4(FROM(from(from(encArg(z0)))), ENCARG(cons_from(cons_from(z0)))) ENCARG(cons_from(cons_from(cons_cons(z0, z1)))) -> c4(FROM(from(cons(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_cons(z0, z1)))) ENCARG(cons_from(cons_from(cons_s(z0)))) -> c4(FROM(from(s(encArg(z0)))), ENCARG(cons_from(cons_s(z0)))) ENCARG(cons_from(cons_from(cons_head(z0)))) -> c4(FROM(from(head(encArg(z0)))), ENCARG(cons_from(cons_head(z0)))) ENCARG(cons_from(cons_from(cons_2nd(z0)))) -> c4(FROM(from(2nd(encArg(z0)))), ENCARG(cons_from(cons_2nd(z0)))) ENCARG(cons_from(cons_from(cons_take(z0, z1)))) -> c4(FROM(from(take(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_take(z0, z1)))) ENCARG(cons_from(cons_from(cons_sel(z0, z1)))) -> c4(FROM(from(sel(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(x0, 0))) -> c4(FROM(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_from(cons_cons(x0, nil))) -> c4(FROM(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_from(cons_cons(x0, cons_active(z0)))) -> c4(FROM(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_from(cons_cons(x0, cons_mark(z0)))) -> c4(FROM(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_from(cons_cons(x0, cons_from(z0)))) -> c4(FROM(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_from(cons_cons(x0, cons_cons(z0, z1)))) -> c4(FROM(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_s(z0)))) -> c4(FROM(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_from(cons_cons(x0, cons_head(z0)))) -> c4(FROM(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_from(cons_cons(x0, cons_2nd(z0)))) -> c4(FROM(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_from(cons_cons(x0, cons_take(z0, z1)))) -> c4(FROM(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_sel(z0, z1)))) -> c4(FROM(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(0, x1))) -> c4(FROM(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_from(cons_cons(nil, x1))) -> c4(FROM(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_from(cons_cons(cons_active(z0), x1))) -> c4(FROM(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_from(cons_cons(cons_mark(z0), x1))) -> c4(FROM(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_from(cons_cons(cons_from(z0), x1))) -> c4(FROM(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_from(cons_cons(cons_cons(z0, z1), x1))) -> c4(FROM(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_s(z0), x1))) -> c4(FROM(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_from(cons_cons(cons_head(z0), x1))) -> c4(FROM(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_from(cons_cons(cons_2nd(z0), x1))) -> c4(FROM(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_from(cons_cons(cons_take(z0, z1), x1))) -> c4(FROM(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_sel(z0, z1), x1))) -> c4(FROM(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1, c11_1 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_from(cons_s(z0))) -> c4(FROM(s(encArg(z0))), ENCARG(cons_s(z0))) by ENCARG(cons_from(cons_s(0))) -> c4(FROM(s(0)), ENCARG(cons_s(0))) ENCARG(cons_from(cons_s(nil))) -> c4(FROM(s(nil)), ENCARG(cons_s(nil))) ENCARG(cons_from(cons_s(cons_active(z0)))) -> c4(FROM(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_from(cons_s(cons_mark(z0)))) -> c4(FROM(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_from(cons_s(cons_from(z0)))) -> c4(FROM(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_from(cons_s(cons_cons(z0, z1)))) -> c4(FROM(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_from(cons_s(cons_s(z0)))) -> c4(FROM(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_from(cons_s(cons_head(z0)))) -> c4(FROM(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_from(cons_s(cons_2nd(z0)))) -> c4(FROM(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_from(cons_s(cons_take(z0, z1)))) -> c4(FROM(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_from(cons_s(cons_sel(z0, z1)))) -> c4(FROM(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c11(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c11(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c11(MARK(mark(nil))) ENCARG(cons_mark(cons_mark(nil))) -> c11(ENCARG(cons_mark(nil))) ENCARG(cons_from(cons_from(cons_active(z0)))) -> c4(FROM(from(active(encArg(z0)))), ENCARG(cons_from(cons_active(z0)))) ENCARG(cons_from(cons_from(cons_mark(z0)))) -> c4(FROM(from(mark(encArg(z0)))), ENCARG(cons_from(cons_mark(z0)))) ENCARG(cons_from(cons_from(cons_from(z0)))) -> c4(FROM(from(from(encArg(z0)))), ENCARG(cons_from(cons_from(z0)))) ENCARG(cons_from(cons_from(cons_cons(z0, z1)))) -> c4(FROM(from(cons(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_cons(z0, z1)))) ENCARG(cons_from(cons_from(cons_s(z0)))) -> c4(FROM(from(s(encArg(z0)))), ENCARG(cons_from(cons_s(z0)))) ENCARG(cons_from(cons_from(cons_head(z0)))) -> c4(FROM(from(head(encArg(z0)))), ENCARG(cons_from(cons_head(z0)))) ENCARG(cons_from(cons_from(cons_2nd(z0)))) -> c4(FROM(from(2nd(encArg(z0)))), ENCARG(cons_from(cons_2nd(z0)))) ENCARG(cons_from(cons_from(cons_take(z0, z1)))) -> c4(FROM(from(take(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_take(z0, z1)))) ENCARG(cons_from(cons_from(cons_sel(z0, z1)))) -> c4(FROM(from(sel(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(x0, 0))) -> c4(FROM(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_from(cons_cons(x0, nil))) -> c4(FROM(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_from(cons_cons(x0, cons_active(z0)))) -> c4(FROM(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_from(cons_cons(x0, cons_mark(z0)))) -> c4(FROM(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_from(cons_cons(x0, cons_from(z0)))) -> c4(FROM(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_from(cons_cons(x0, cons_cons(z0, z1)))) -> c4(FROM(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_s(z0)))) -> c4(FROM(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_from(cons_cons(x0, cons_head(z0)))) -> c4(FROM(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_from(cons_cons(x0, cons_2nd(z0)))) -> c4(FROM(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_from(cons_cons(x0, cons_take(z0, z1)))) -> c4(FROM(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_sel(z0, z1)))) -> c4(FROM(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(0, x1))) -> c4(FROM(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_from(cons_cons(nil, x1))) -> c4(FROM(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_from(cons_cons(cons_active(z0), x1))) -> c4(FROM(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_from(cons_cons(cons_mark(z0), x1))) -> c4(FROM(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_from(cons_cons(cons_from(z0), x1))) -> c4(FROM(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_from(cons_cons(cons_cons(z0, z1), x1))) -> c4(FROM(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_s(z0), x1))) -> c4(FROM(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_from(cons_cons(cons_head(z0), x1))) -> c4(FROM(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_from(cons_cons(cons_2nd(z0), x1))) -> c4(FROM(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_from(cons_cons(cons_take(z0, z1), x1))) -> c4(FROM(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_sel(z0, z1), x1))) -> c4(FROM(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_from(cons_s(0))) -> c4(FROM(s(0)), ENCARG(cons_s(0))) ENCARG(cons_from(cons_s(nil))) -> c4(FROM(s(nil)), ENCARG(cons_s(nil))) ENCARG(cons_from(cons_s(cons_active(z0)))) -> c4(FROM(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_from(cons_s(cons_mark(z0)))) -> c4(FROM(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_from(cons_s(cons_from(z0)))) -> c4(FROM(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_from(cons_s(cons_cons(z0, z1)))) -> c4(FROM(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_from(cons_s(cons_s(z0)))) -> c4(FROM(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_from(cons_s(cons_head(z0)))) -> c4(FROM(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_from(cons_s(cons_2nd(z0)))) -> c4(FROM(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_from(cons_s(cons_take(z0, z1)))) -> c4(FROM(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_from(cons_s(cons_sel(z0, z1)))) -> c4(FROM(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1, c11_1 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_from(cons_s(nil))) -> c4(FROM(s(nil)), ENCARG(cons_s(nil))) ENCARG(cons_from(cons_s(0))) -> c4(FROM(s(0)), ENCARG(cons_s(0))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: encArg(0) -> 0 encArg(nil) -> nil encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_from(z0)) -> from(encArg(z0)) encArg(cons_cons(z0, z1)) -> cons(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_head(z0)) -> head(encArg(z0)) encArg(cons_2nd(z0)) -> 2nd(encArg(z0)) encArg(cons_take(z0, z1)) -> take(encArg(z0), encArg(z1)) encArg(cons_sel(z0, z1)) -> sel(encArg(z0), encArg(z1)) active(from(z0)) -> mark(cons(z0, from(s(z0)))) active(head(cons(z0, z1))) -> mark(z0) active(2nd(cons(z0, z1))) -> mark(head(z1)) active(take(0, z0)) -> mark(nil) active(take(s(z0), cons(z1, z2))) -> mark(cons(z1, take(z0, z2))) active(sel(0, cons(z0, z1))) -> mark(z0) active(sel(s(z0), cons(z1, z2))) -> mark(sel(z0, z2)) mark(from(z0)) -> active(from(mark(z0))) mark(cons(z0, z1)) -> active(cons(mark(z0), z1)) mark(s(z0)) -> active(s(mark(z0))) mark(head(z0)) -> active(head(mark(z0))) mark(2nd(z0)) -> active(2nd(mark(z0))) mark(take(z0, z1)) -> active(take(mark(z0), mark(z1))) mark(0) -> active(0) mark(nil) -> active(nil) mark(sel(z0, z1)) -> active(sel(mark(z0), mark(z1))) from(mark(z0)) -> from(z0) from(active(z0)) -> from(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) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) head(mark(z0)) -> head(z0) head(active(z0)) -> head(z0) 2nd(mark(z0)) -> 2nd(z0) 2nd(active(z0)) -> 2nd(z0) take(mark(z0), z1) -> take(z0, z1) take(z0, mark(z1)) -> take(z0, z1) take(active(z0), z1) -> take(z0, z1) take(z0, active(z1)) -> take(z0, z1) 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) Tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 ENCARG(cons_active(cons_from(z0))) -> c2(ACTIVE(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_from(z0))) -> c3(MARK(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_mark(cons_cons(z0, z1))) -> c3(MARK(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_head(z0))) -> c3(MARK(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_mark(cons_2nd(z0))) -> c3(MARK(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_mark(cons_take(z0, z1))) -> c3(MARK(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_mark(cons_sel(z0, z1))) -> c3(MARK(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_mark(nil)) -> c3(MARK(nil)) ENCARG(cons_from(cons_active(z0))) -> c4(FROM(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_from(cons_mark(z0))) -> c4(FROM(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_from(cons_head(z0))) -> c4(FROM(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_from(cons_2nd(z0))) -> c4(FROM(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_from(cons_take(z0, z1))) -> c4(FROM(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_from(cons_sel(z0, z1))) -> c4(FROM(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(x0, cons_active(z0))) -> c5(CONS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_cons(x0, cons_mark(z0))) -> c5(CONS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_cons(x0, cons_from(z0))) -> c5(CONS(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_cons(x0, cons_cons(z0, z1))) -> c5(CONS(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_cons(x0, cons_s(z0))) -> c5(CONS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_cons(x0, cons_head(z0))) -> c5(CONS(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_cons(x0, cons_2nd(z0))) -> c5(CONS(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_cons(x0, cons_take(z0, z1))) -> c5(CONS(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_cons(x0, cons_sel(z0, z1))) -> c5(CONS(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_cons(cons_active(z0), x1)) -> c5(CONS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_mark(z0), x1)) -> c5(CONS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_from(z0), x1)) -> c5(CONS(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_cons(z0, z1), x1)) -> c5(CONS(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_s(z0), x1)) -> c5(CONS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_head(z0), x1)) -> c5(CONS(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_2nd(z0), x1)) -> c5(CONS(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_cons(cons_take(z0, z1), x1)) -> c5(CONS(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(cons_sel(z0, z1), x1)) -> c5(CONS(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_cons(x0, 0)) -> c5(CONS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_cons(x0, nil)) -> c5(CONS(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_cons(0, x1)) -> c5(CONS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_cons(nil, x1)) -> c5(CONS(nil, 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_from(z0))) -> c6(S(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_s(cons_cons(z0, z1))) -> c6(S(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_head(z0))) -> c6(S(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_s(cons_2nd(z0))) -> c6(S(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_s(cons_take(z0, z1))) -> c6(S(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_s(cons_sel(z0, z1))) -> c6(S(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_head(cons_active(z0))) -> c7(HEAD(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_head(cons_mark(z0))) -> c7(HEAD(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_head(cons_from(z0))) -> c7(HEAD(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_head(cons_cons(z0, z1))) -> c7(HEAD(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_head(cons_s(z0))) -> c7(HEAD(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_head(cons_head(z0))) -> c7(HEAD(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_head(cons_2nd(z0))) -> c7(HEAD(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_head(cons_take(z0, z1))) -> c7(HEAD(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_head(cons_sel(z0, z1))) -> c7(HEAD(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_2nd(cons_active(z0))) -> c8(2ND(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_2nd(cons_mark(z0))) -> c8(2ND(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_2nd(cons_from(z0))) -> c8(2ND(from(encArg(z0))), ENCARG(cons_from(z0))) ENCARG(cons_2nd(cons_cons(z0, z1))) -> c8(2ND(cons(encArg(z0), encArg(z1))), ENCARG(cons_cons(z0, z1))) ENCARG(cons_2nd(cons_s(z0))) -> c8(2ND(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_2nd(cons_head(z0))) -> c8(2ND(head(encArg(z0))), ENCARG(cons_head(z0))) ENCARG(cons_2nd(cons_2nd(z0))) -> c8(2ND(2nd(encArg(z0))), ENCARG(cons_2nd(z0))) ENCARG(cons_2nd(cons_take(z0, z1))) -> c8(2ND(take(encArg(z0), encArg(z1))), ENCARG(cons_take(z0, z1))) ENCARG(cons_2nd(cons_sel(z0, z1))) -> c8(2ND(sel(encArg(z0), encArg(z1))), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(x0, cons_active(z0))) -> c9(TAKE(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_take(x0, cons_mark(z0))) -> c9(TAKE(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_take(x0, cons_from(z0))) -> c9(TAKE(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_take(x0, cons_cons(z0, z1))) -> c9(TAKE(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_take(x0, cons_s(z0))) -> c9(TAKE(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_take(x0, cons_head(z0))) -> c9(TAKE(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_take(x0, cons_2nd(z0))) -> c9(TAKE(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_take(x0, cons_take(z0, z1))) -> c9(TAKE(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_take(x0, cons_sel(z0, z1))) -> c9(TAKE(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_take(cons_active(z0), x1)) -> c9(TAKE(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_take(cons_mark(z0), x1)) -> c9(TAKE(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_take(cons_from(z0), x1)) -> c9(TAKE(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_take(cons_cons(z0, z1), x1)) -> c9(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_s(z0), x1)) -> c9(TAKE(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_take(cons_head(z0), x1)) -> c9(TAKE(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_take(cons_2nd(z0), x1)) -> c9(TAKE(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_take(cons_take(z0, z1), x1)) -> c9(TAKE(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_take(cons_sel(z0, z1), x1)) -> c9(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_take(x0, 0)) -> c9(TAKE(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_take(x0, nil)) -> c9(TAKE(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_take(0, x1)) -> c9(TAKE(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_take(nil, x1)) -> c9(TAKE(nil, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(x0, cons_active(z0))) -> c10(SEL(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_sel(x0, cons_mark(z0))) -> c10(SEL(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_sel(x0, cons_from(z0))) -> c10(SEL(encArg(x0), from(encArg(z0))), ENCARG(x0), ENCARG(cons_from(z0))) ENCARG(cons_sel(x0, cons_cons(z0, z1))) -> c10(SEL(encArg(x0), cons(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_cons(z0, z1))) ENCARG(cons_sel(x0, cons_s(z0))) -> c10(SEL(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_sel(x0, cons_head(z0))) -> c10(SEL(encArg(x0), head(encArg(z0))), ENCARG(x0), ENCARG(cons_head(z0))) ENCARG(cons_sel(x0, cons_2nd(z0))) -> c10(SEL(encArg(x0), 2nd(encArg(z0))), ENCARG(x0), ENCARG(cons_2nd(z0))) ENCARG(cons_sel(x0, cons_take(z0, z1))) -> c10(SEL(encArg(x0), take(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_take(z0, z1))) ENCARG(cons_sel(x0, cons_sel(z0, z1))) -> c10(SEL(encArg(x0), sel(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_sel(z0, z1))) ENCARG(cons_sel(cons_active(z0), x1)) -> c10(SEL(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_mark(z0), x1)) -> c10(SEL(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_from(z0), x1)) -> c10(SEL(from(encArg(z0)), encArg(x1)), ENCARG(cons_from(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_cons(z0, z1), x1)) -> c10(SEL(cons(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_cons(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_s(z0), x1)) -> c10(SEL(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_head(z0), x1)) -> c10(SEL(head(encArg(z0)), encArg(x1)), ENCARG(cons_head(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_2nd(z0), x1)) -> c10(SEL(2nd(encArg(z0)), encArg(x1)), ENCARG(cons_2nd(z0)), ENCARG(x1)) ENCARG(cons_sel(cons_take(z0, z1), x1)) -> c10(SEL(take(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_take(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(cons_sel(z0, z1), x1)) -> c10(SEL(sel(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_sel(z0, z1)), ENCARG(x1)) ENCARG(cons_sel(x0, 0)) -> c10(SEL(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_sel(x0, nil)) -> c10(SEL(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_sel(0, x1)) -> c10(SEL(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_sel(nil, x1)) -> c10(SEL(nil, encArg(x1)), ENCARG(x1)) MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(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_from(z0)) -> c(ACTIVE(from(encArg(z0)))) ENCODE_ACTIVE(cons_cons(z0, z1)) -> c(ACTIVE(cons(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_head(z0)) -> c(ACTIVE(head(encArg(z0)))) ENCODE_ACTIVE(cons_2nd(z0)) -> c(ACTIVE(2nd(encArg(z0)))) ENCODE_ACTIVE(cons_take(z0, z1)) -> c(ACTIVE(take(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_sel(z0, z1)) -> c(ACTIVE(sel(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_active(z0)) -> c(FROM(active(encArg(z0)))) ENCODE_FROM(cons_mark(z0)) -> c(FROM(mark(encArg(z0)))) ENCODE_FROM(cons_from(z0)) -> c(FROM(from(encArg(z0)))) ENCODE_FROM(cons_cons(z0, z1)) -> c(FROM(cons(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_s(z0)) -> c(FROM(s(encArg(z0)))) ENCODE_FROM(cons_head(z0)) -> c(FROM(head(encArg(z0)))) ENCODE_FROM(cons_2nd(z0)) -> c(FROM(2nd(encArg(z0)))) ENCODE_FROM(cons_take(z0, z1)) -> c(FROM(take(encArg(z0), encArg(z1)))) ENCODE_FROM(cons_sel(z0, z1)) -> c(FROM(sel(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_from(z0)) -> c(MARK(from(encArg(z0)))) ENCODE_MARK(cons_cons(z0, z1)) -> c(MARK(cons(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_head(z0)) -> c(MARK(head(encArg(z0)))) ENCODE_MARK(cons_2nd(z0)) -> c(MARK(2nd(encArg(z0)))) ENCODE_MARK(cons_take(z0, z1)) -> c(MARK(take(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_sel(z0, z1)) -> c(MARK(sel(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, 0) -> c(CONS(encArg(x0), 0)) ENCODE_CONS(x0, nil) -> c(CONS(encArg(x0), nil)) 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_from(z0)) -> c(CONS(encArg(x0), from(encArg(z0)))) ENCODE_CONS(x0, cons_cons(z0, z1)) -> c(CONS(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_s(z0)) -> c(CONS(encArg(x0), s(encArg(z0)))) ENCODE_CONS(x0, cons_head(z0)) -> c(CONS(encArg(x0), head(encArg(z0)))) ENCODE_CONS(x0, cons_2nd(z0)) -> c(CONS(encArg(x0), 2nd(encArg(z0)))) ENCODE_CONS(x0, cons_take(z0, z1)) -> c(CONS(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_CONS(x0, cons_sel(z0, z1)) -> c(CONS(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_CONS(0, x1) -> c(CONS(0, encArg(x1))) ENCODE_CONS(nil, x1) -> c(CONS(nil, 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_from(z0), x1) -> c(CONS(from(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_cons(z0, z1), x1) -> c(CONS(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_s(z0), x1) -> c(CONS(s(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_head(z0), x1) -> c(CONS(head(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_2nd(z0), x1) -> c(CONS(2nd(encArg(z0)), encArg(x1))) ENCODE_CONS(cons_take(z0, z1), x1) -> c(CONS(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_CONS(cons_sel(z0, z1), x1) -> c(CONS(sel(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_from(z0)) -> c(S(from(encArg(z0)))) ENCODE_S(cons_cons(z0, z1)) -> c(S(cons(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_head(z0)) -> c(S(head(encArg(z0)))) ENCODE_S(cons_2nd(z0)) -> c(S(2nd(encArg(z0)))) ENCODE_S(cons_take(z0, z1)) -> c(S(take(encArg(z0), encArg(z1)))) ENCODE_S(cons_sel(z0, z1)) -> c(S(sel(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_active(z0)) -> c(HEAD(active(encArg(z0)))) ENCODE_HEAD(cons_mark(z0)) -> c(HEAD(mark(encArg(z0)))) ENCODE_HEAD(cons_from(z0)) -> c(HEAD(from(encArg(z0)))) ENCODE_HEAD(cons_cons(z0, z1)) -> c(HEAD(cons(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_s(z0)) -> c(HEAD(s(encArg(z0)))) ENCODE_HEAD(cons_head(z0)) -> c(HEAD(head(encArg(z0)))) ENCODE_HEAD(cons_2nd(z0)) -> c(HEAD(2nd(encArg(z0)))) ENCODE_HEAD(cons_take(z0, z1)) -> c(HEAD(take(encArg(z0), encArg(z1)))) ENCODE_HEAD(cons_sel(z0, z1)) -> c(HEAD(sel(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_active(z0)) -> c(2ND(active(encArg(z0)))) ENCODE_2ND(cons_mark(z0)) -> c(2ND(mark(encArg(z0)))) ENCODE_2ND(cons_from(z0)) -> c(2ND(from(encArg(z0)))) ENCODE_2ND(cons_cons(z0, z1)) -> c(2ND(cons(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_s(z0)) -> c(2ND(s(encArg(z0)))) ENCODE_2ND(cons_head(z0)) -> c(2ND(head(encArg(z0)))) ENCODE_2ND(cons_2nd(z0)) -> c(2ND(2nd(encArg(z0)))) ENCODE_2ND(cons_take(z0, z1)) -> c(2ND(take(encArg(z0), encArg(z1)))) ENCODE_2ND(cons_sel(z0, z1)) -> c(2ND(sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, 0) -> c(TAKE(encArg(x0), 0)) ENCODE_TAKE(x0, nil) -> c(TAKE(encArg(x0), nil)) ENCODE_TAKE(x0, cons_active(z0)) -> c(TAKE(encArg(x0), active(encArg(z0)))) ENCODE_TAKE(x0, cons_mark(z0)) -> c(TAKE(encArg(x0), mark(encArg(z0)))) ENCODE_TAKE(x0, cons_from(z0)) -> c(TAKE(encArg(x0), from(encArg(z0)))) ENCODE_TAKE(x0, cons_cons(z0, z1)) -> c(TAKE(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_s(z0)) -> c(TAKE(encArg(x0), s(encArg(z0)))) ENCODE_TAKE(x0, cons_head(z0)) -> c(TAKE(encArg(x0), head(encArg(z0)))) ENCODE_TAKE(x0, cons_2nd(z0)) -> c(TAKE(encArg(x0), 2nd(encArg(z0)))) ENCODE_TAKE(x0, cons_take(z0, z1)) -> c(TAKE(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_TAKE(x0, cons_sel(z0, z1)) -> c(TAKE(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_TAKE(0, x1) -> c(TAKE(0, encArg(x1))) ENCODE_TAKE(nil, x1) -> c(TAKE(nil, encArg(x1))) ENCODE_TAKE(cons_active(z0), x1) -> c(TAKE(active(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_mark(z0), x1) -> c(TAKE(mark(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_from(z0), x1) -> c(TAKE(from(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_cons(z0, z1), x1) -> c(TAKE(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_s(z0), x1) -> c(TAKE(s(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_head(z0), x1) -> c(TAKE(head(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_2nd(z0), x1) -> c(TAKE(2nd(encArg(z0)), encArg(x1))) ENCODE_TAKE(cons_take(z0, z1), x1) -> c(TAKE(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_TAKE(cons_sel(z0, z1), x1) -> c(TAKE(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(x0, 0) -> c(SEL(encArg(x0), 0)) ENCODE_SEL(x0, nil) -> c(SEL(encArg(x0), nil)) 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_from(z0)) -> c(SEL(encArg(x0), from(encArg(z0)))) ENCODE_SEL(x0, cons_cons(z0, z1)) -> c(SEL(encArg(x0), cons(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_s(z0)) -> c(SEL(encArg(x0), s(encArg(z0)))) ENCODE_SEL(x0, cons_head(z0)) -> c(SEL(encArg(x0), head(encArg(z0)))) ENCODE_SEL(x0, cons_2nd(z0)) -> c(SEL(encArg(x0), 2nd(encArg(z0)))) ENCODE_SEL(x0, cons_take(z0, z1)) -> c(SEL(encArg(x0), take(encArg(z0), encArg(z1)))) ENCODE_SEL(x0, cons_sel(z0, z1)) -> c(SEL(encArg(x0), sel(encArg(z0), encArg(z1)))) ENCODE_SEL(0, x1) -> c(SEL(0, encArg(x1))) ENCODE_SEL(nil, x1) -> c(SEL(nil, 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_from(z0), x1) -> c(SEL(from(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_cons(z0, z1), x1) -> c(SEL(cons(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_s(z0), x1) -> c(SEL(s(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_head(z0), x1) -> c(SEL(head(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_2nd(z0), x1) -> c(SEL(2nd(encArg(z0)), encArg(x1))) ENCODE_SEL(cons_take(z0, z1), x1) -> c(SEL(take(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_SEL(cons_sel(z0, z1), x1) -> c(SEL(sel(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(cons_active(z0)))) -> c2(ACTIVE(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_active(cons_active(cons_mark(z0)))) -> c2(ACTIVE(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_active(cons_active(cons_from(z0)))) -> c2(ACTIVE(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_active(cons_active(cons_cons(z0, z1)))) -> c2(ACTIVE(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_head(z0)))) -> c2(ACTIVE(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_active(cons_active(cons_2nd(z0)))) -> c2(ACTIVE(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_active(cons_active(cons_take(z0, z1)))) -> c2(ACTIVE(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_active(cons_active(cons_sel(z0, z1)))) -> c2(ACTIVE(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(cons_active(z0)))) -> c2(ACTIVE(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_active(cons_mark(cons_mark(z0)))) -> c2(ACTIVE(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_active(cons_mark(cons_from(z0)))) -> c2(ACTIVE(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_active(cons_mark(cons_cons(z0, z1)))) -> c2(ACTIVE(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_active(cons_mark(cons_s(z0)))) -> c2(ACTIVE(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_active(cons_mark(cons_head(z0)))) -> c2(ACTIVE(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_active(cons_mark(cons_2nd(z0)))) -> c2(ACTIVE(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_active(cons_mark(cons_take(z0, z1)))) -> c2(ACTIVE(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_active(cons_mark(cons_sel(z0, z1)))) -> c2(ACTIVE(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) ENCARG(cons_active(cons_mark(nil))) -> c1(ACTIVE(mark(nil))) ENCARG(cons_active(cons_mark(nil))) -> c1(ENCARG(cons_mark(nil))) ENCARG(cons_active(cons_cons(x0, 0))) -> c2(ACTIVE(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_active(cons_cons(x0, nil))) -> c2(ACTIVE(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_active(cons_cons(x0, cons_active(z0)))) -> c2(ACTIVE(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_active(cons_cons(x0, cons_mark(z0)))) -> c2(ACTIVE(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_active(cons_cons(x0, cons_from(z0)))) -> c2(ACTIVE(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_active(cons_cons(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_s(z0)))) -> c2(ACTIVE(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_active(cons_cons(x0, cons_head(z0)))) -> c2(ACTIVE(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_active(cons_cons(x0, cons_2nd(z0)))) -> c2(ACTIVE(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_cons(x0, cons_take(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_cons(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_cons(0, x1))) -> c2(ACTIVE(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_active(cons_cons(nil, x1))) -> c2(ACTIVE(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_active(cons_cons(cons_active(z0), x1))) -> c2(ACTIVE(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_active(cons_cons(cons_mark(z0), x1))) -> c2(ACTIVE(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_active(cons_cons(cons_from(z0), x1))) -> c2(ACTIVE(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_active(cons_cons(cons_cons(z0, z1), x1))) -> c2(ACTIVE(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_s(z0), x1))) -> c2(ACTIVE(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_active(cons_cons(cons_head(z0), x1))) -> c2(ACTIVE(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_active(cons_cons(cons_2nd(z0), x1))) -> c2(ACTIVE(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_active(cons_cons(cons_take(z0, z1), x1))) -> c2(ACTIVE(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_cons(cons_sel(z0, z1), x1))) -> c2(ACTIVE(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_from(z0)))) -> c2(ACTIVE(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_active(cons_s(cons_cons(z0, z1)))) -> c2(ACTIVE(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_head(z0)))) -> c2(ACTIVE(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_active(cons_s(cons_2nd(z0)))) -> c2(ACTIVE(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_active(cons_s(cons_take(z0, z1)))) -> c2(ACTIVE(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_active(cons_s(cons_sel(z0, z1)))) -> c2(ACTIVE(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) ENCARG(cons_active(cons_head(cons_active(z0)))) -> c2(ACTIVE(head(active(encArg(z0)))), ENCARG(cons_head(cons_active(z0)))) ENCARG(cons_active(cons_head(cons_mark(z0)))) -> c2(ACTIVE(head(mark(encArg(z0)))), ENCARG(cons_head(cons_mark(z0)))) ENCARG(cons_active(cons_head(cons_from(z0)))) -> c2(ACTIVE(head(from(encArg(z0)))), ENCARG(cons_head(cons_from(z0)))) ENCARG(cons_active(cons_head(cons_cons(z0, z1)))) -> c2(ACTIVE(head(cons(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_cons(z0, z1)))) ENCARG(cons_active(cons_head(cons_s(z0)))) -> c2(ACTIVE(head(s(encArg(z0)))), ENCARG(cons_head(cons_s(z0)))) ENCARG(cons_active(cons_head(cons_head(z0)))) -> c2(ACTIVE(head(head(encArg(z0)))), ENCARG(cons_head(cons_head(z0)))) ENCARG(cons_active(cons_head(cons_2nd(z0)))) -> c2(ACTIVE(head(2nd(encArg(z0)))), ENCARG(cons_head(cons_2nd(z0)))) ENCARG(cons_active(cons_head(cons_take(z0, z1)))) -> c2(ACTIVE(head(take(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_take(z0, z1)))) ENCARG(cons_active(cons_head(cons_sel(z0, z1)))) -> c2(ACTIVE(head(sel(encArg(z0), encArg(z1)))), ENCARG(cons_head(cons_sel(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_active(z0)))) -> c2(ACTIVE(2nd(active(encArg(z0)))), ENCARG(cons_2nd(cons_active(z0)))) ENCARG(cons_active(cons_2nd(cons_mark(z0)))) -> c2(ACTIVE(2nd(mark(encArg(z0)))), ENCARG(cons_2nd(cons_mark(z0)))) ENCARG(cons_active(cons_2nd(cons_from(z0)))) -> c2(ACTIVE(2nd(from(encArg(z0)))), ENCARG(cons_2nd(cons_from(z0)))) ENCARG(cons_active(cons_2nd(cons_cons(z0, z1)))) -> c2(ACTIVE(2nd(cons(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_cons(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_s(z0)))) -> c2(ACTIVE(2nd(s(encArg(z0)))), ENCARG(cons_2nd(cons_s(z0)))) ENCARG(cons_active(cons_2nd(cons_head(z0)))) -> c2(ACTIVE(2nd(head(encArg(z0)))), ENCARG(cons_2nd(cons_head(z0)))) ENCARG(cons_active(cons_2nd(cons_2nd(z0)))) -> c2(ACTIVE(2nd(2nd(encArg(z0)))), ENCARG(cons_2nd(cons_2nd(z0)))) ENCARG(cons_active(cons_2nd(cons_take(z0, z1)))) -> c2(ACTIVE(2nd(take(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_take(z0, z1)))) ENCARG(cons_active(cons_2nd(cons_sel(z0, z1)))) -> c2(ACTIVE(2nd(sel(encArg(z0), encArg(z1)))), ENCARG(cons_2nd(cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(x0, 0))) -> c2(ACTIVE(take(encArg(x0), 0)), ENCARG(cons_take(x0, 0))) ENCARG(cons_active(cons_take(x0, nil))) -> c2(ACTIVE(take(encArg(x0), nil)), ENCARG(cons_take(x0, nil))) ENCARG(cons_active(cons_take(x0, cons_active(z0)))) -> c2(ACTIVE(take(encArg(x0), active(encArg(z0)))), ENCARG(cons_take(x0, cons_active(z0)))) ENCARG(cons_active(cons_take(x0, cons_mark(z0)))) -> c2(ACTIVE(take(encArg(x0), mark(encArg(z0)))), ENCARG(cons_take(x0, cons_mark(z0)))) ENCARG(cons_active(cons_take(x0, cons_from(z0)))) -> c2(ACTIVE(take(encArg(x0), from(encArg(z0)))), ENCARG(cons_take(x0, cons_from(z0)))) ENCARG(cons_active(cons_take(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_s(z0)))) -> c2(ACTIVE(take(encArg(x0), s(encArg(z0)))), ENCARG(cons_take(x0, cons_s(z0)))) ENCARG(cons_active(cons_take(x0, cons_head(z0)))) -> c2(ACTIVE(take(encArg(x0), head(encArg(z0)))), ENCARG(cons_take(x0, cons_head(z0)))) ENCARG(cons_active(cons_take(x0, cons_2nd(z0)))) -> c2(ACTIVE(take(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_take(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_take(x0, cons_take(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_take(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(take(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_take(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_take(0, x1))) -> c2(ACTIVE(take(0, encArg(x1))), ENCARG(cons_take(0, x1))) ENCARG(cons_active(cons_take(nil, x1))) -> c2(ACTIVE(take(nil, encArg(x1))), ENCARG(cons_take(nil, x1))) ENCARG(cons_active(cons_take(cons_active(z0), x1))) -> c2(ACTIVE(take(active(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_active(z0), x1))) ENCARG(cons_active(cons_take(cons_mark(z0), x1))) -> c2(ACTIVE(take(mark(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_mark(z0), x1))) ENCARG(cons_active(cons_take(cons_from(z0), x1))) -> c2(ACTIVE(take(from(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_from(z0), x1))) ENCARG(cons_active(cons_take(cons_cons(z0, z1), x1))) -> c2(ACTIVE(take(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_s(z0), x1))) -> c2(ACTIVE(take(s(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_s(z0), x1))) ENCARG(cons_active(cons_take(cons_head(z0), x1))) -> c2(ACTIVE(take(head(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_head(z0), x1))) ENCARG(cons_active(cons_take(cons_2nd(z0), x1))) -> c2(ACTIVE(take(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_take(cons_2nd(z0), x1))) ENCARG(cons_active(cons_take(cons_take(z0, z1), x1))) -> c2(ACTIVE(take(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_take(cons_sel(z0, z1), x1))) -> c2(ACTIVE(take(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_take(cons_sel(z0, z1), x1))) ENCARG(cons_active(cons_sel(x0, 0))) -> c2(ACTIVE(sel(encArg(x0), 0)), ENCARG(cons_sel(x0, 0))) ENCARG(cons_active(cons_sel(x0, nil))) -> c2(ACTIVE(sel(encArg(x0), nil)), ENCARG(cons_sel(x0, nil))) ENCARG(cons_active(cons_sel(x0, cons_active(z0)))) -> c2(ACTIVE(sel(encArg(x0), active(encArg(z0)))), ENCARG(cons_sel(x0, cons_active(z0)))) ENCARG(cons_active(cons_sel(x0, cons_mark(z0)))) -> c2(ACTIVE(sel(encArg(x0), mark(encArg(z0)))), ENCARG(cons_sel(x0, cons_mark(z0)))) ENCARG(cons_active(cons_sel(x0, cons_from(z0)))) -> c2(ACTIVE(sel(encArg(x0), from(encArg(z0)))), ENCARG(cons_sel(x0, cons_from(z0)))) ENCARG(cons_active(cons_sel(x0, cons_cons(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_cons(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_s(z0)))) -> c2(ACTIVE(sel(encArg(x0), s(encArg(z0)))), ENCARG(cons_sel(x0, cons_s(z0)))) ENCARG(cons_active(cons_sel(x0, cons_head(z0)))) -> c2(ACTIVE(sel(encArg(x0), head(encArg(z0)))), ENCARG(cons_sel(x0, cons_head(z0)))) ENCARG(cons_active(cons_sel(x0, cons_2nd(z0)))) -> c2(ACTIVE(sel(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_sel(x0, cons_2nd(z0)))) ENCARG(cons_active(cons_sel(x0, cons_take(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_take(z0, z1)))) ENCARG(cons_active(cons_sel(x0, cons_sel(z0, z1)))) -> c2(ACTIVE(sel(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_sel(x0, cons_sel(z0, z1)))) ENCARG(cons_active(cons_sel(0, x1))) -> c2(ACTIVE(sel(0, encArg(x1))), ENCARG(cons_sel(0, x1))) ENCARG(cons_active(cons_sel(nil, x1))) -> c2(ACTIVE(sel(nil, encArg(x1))), ENCARG(cons_sel(nil, x1))) ENCARG(cons_active(cons_sel(cons_active(z0), x1))) -> c2(ACTIVE(sel(active(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_active(z0), x1))) ENCARG(cons_active(cons_sel(cons_mark(z0), x1))) -> c2(ACTIVE(sel(mark(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_mark(z0), x1))) ENCARG(cons_active(cons_sel(cons_from(z0), x1))) -> c2(ACTIVE(sel(from(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_from(z0), x1))) ENCARG(cons_active(cons_sel(cons_cons(z0, z1), x1))) -> c2(ACTIVE(sel(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_cons(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_s(z0), x1))) -> c2(ACTIVE(sel(s(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_s(z0), x1))) ENCARG(cons_active(cons_sel(cons_head(z0), x1))) -> c2(ACTIVE(sel(head(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_head(z0), x1))) ENCARG(cons_active(cons_sel(cons_2nd(z0), x1))) -> c2(ACTIVE(sel(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_sel(cons_2nd(z0), x1))) ENCARG(cons_active(cons_sel(cons_take(z0, z1), x1))) -> c2(ACTIVE(sel(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_take(z0, z1), x1))) ENCARG(cons_active(cons_sel(cons_sel(z0, z1), x1))) -> c2(ACTIVE(sel(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_sel(cons_sel(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_from(z0)))) -> c3(MARK(active(from(encArg(z0)))), ENCARG(cons_active(cons_from(z0)))) ENCARG(cons_mark(cons_active(cons_cons(z0, z1)))) -> c3(MARK(active(cons(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_head(z0)))) -> c3(MARK(active(head(encArg(z0)))), ENCARG(cons_active(cons_head(z0)))) ENCARG(cons_mark(cons_active(cons_2nd(z0)))) -> c3(MARK(active(2nd(encArg(z0)))), ENCARG(cons_active(cons_2nd(z0)))) ENCARG(cons_mark(cons_active(cons_take(z0, z1)))) -> c3(MARK(active(take(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_take(z0, z1)))) ENCARG(cons_mark(cons_active(cons_sel(z0, z1)))) -> c3(MARK(active(sel(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_from(z0)))) -> c3(MARK(mark(from(encArg(z0)))), ENCARG(cons_mark(cons_from(z0)))) ENCARG(cons_mark(cons_mark(cons_cons(z0, z1)))) -> c3(MARK(mark(cons(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_cons(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_head(z0)))) -> c3(MARK(mark(head(encArg(z0)))), ENCARG(cons_mark(cons_head(z0)))) ENCARG(cons_mark(cons_mark(cons_2nd(z0)))) -> c3(MARK(mark(2nd(encArg(z0)))), ENCARG(cons_mark(cons_2nd(z0)))) ENCARG(cons_mark(cons_mark(cons_take(z0, z1)))) -> c3(MARK(mark(take(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_take(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_sel(z0, z1)))) -> c3(MARK(mark(sel(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_sel(z0, z1)))) ENCARG(cons_mark(cons_mark(0))) -> c11(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c11(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(nil))) -> c11(MARK(mark(nil))) ENCARG(cons_mark(cons_mark(nil))) -> c11(ENCARG(cons_mark(nil))) ENCARG(cons_from(cons_from(cons_active(z0)))) -> c4(FROM(from(active(encArg(z0)))), ENCARG(cons_from(cons_active(z0)))) ENCARG(cons_from(cons_from(cons_mark(z0)))) -> c4(FROM(from(mark(encArg(z0)))), ENCARG(cons_from(cons_mark(z0)))) ENCARG(cons_from(cons_from(cons_from(z0)))) -> c4(FROM(from(from(encArg(z0)))), ENCARG(cons_from(cons_from(z0)))) ENCARG(cons_from(cons_from(cons_cons(z0, z1)))) -> c4(FROM(from(cons(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_cons(z0, z1)))) ENCARG(cons_from(cons_from(cons_s(z0)))) -> c4(FROM(from(s(encArg(z0)))), ENCARG(cons_from(cons_s(z0)))) ENCARG(cons_from(cons_from(cons_head(z0)))) -> c4(FROM(from(head(encArg(z0)))), ENCARG(cons_from(cons_head(z0)))) ENCARG(cons_from(cons_from(cons_2nd(z0)))) -> c4(FROM(from(2nd(encArg(z0)))), ENCARG(cons_from(cons_2nd(z0)))) ENCARG(cons_from(cons_from(cons_take(z0, z1)))) -> c4(FROM(from(take(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_take(z0, z1)))) ENCARG(cons_from(cons_from(cons_sel(z0, z1)))) -> c4(FROM(from(sel(encArg(z0), encArg(z1)))), ENCARG(cons_from(cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(x0, 0))) -> c4(FROM(cons(encArg(x0), 0)), ENCARG(cons_cons(x0, 0))) ENCARG(cons_from(cons_cons(x0, nil))) -> c4(FROM(cons(encArg(x0), nil)), ENCARG(cons_cons(x0, nil))) ENCARG(cons_from(cons_cons(x0, cons_active(z0)))) -> c4(FROM(cons(encArg(x0), active(encArg(z0)))), ENCARG(cons_cons(x0, cons_active(z0)))) ENCARG(cons_from(cons_cons(x0, cons_mark(z0)))) -> c4(FROM(cons(encArg(x0), mark(encArg(z0)))), ENCARG(cons_cons(x0, cons_mark(z0)))) ENCARG(cons_from(cons_cons(x0, cons_from(z0)))) -> c4(FROM(cons(encArg(x0), from(encArg(z0)))), ENCARG(cons_cons(x0, cons_from(z0)))) ENCARG(cons_from(cons_cons(x0, cons_cons(z0, z1)))) -> c4(FROM(cons(encArg(x0), cons(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_cons(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_s(z0)))) -> c4(FROM(cons(encArg(x0), s(encArg(z0)))), ENCARG(cons_cons(x0, cons_s(z0)))) ENCARG(cons_from(cons_cons(x0, cons_head(z0)))) -> c4(FROM(cons(encArg(x0), head(encArg(z0)))), ENCARG(cons_cons(x0, cons_head(z0)))) ENCARG(cons_from(cons_cons(x0, cons_2nd(z0)))) -> c4(FROM(cons(encArg(x0), 2nd(encArg(z0)))), ENCARG(cons_cons(x0, cons_2nd(z0)))) ENCARG(cons_from(cons_cons(x0, cons_take(z0, z1)))) -> c4(FROM(cons(encArg(x0), take(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_take(z0, z1)))) ENCARG(cons_from(cons_cons(x0, cons_sel(z0, z1)))) -> c4(FROM(cons(encArg(x0), sel(encArg(z0), encArg(z1)))), ENCARG(cons_cons(x0, cons_sel(z0, z1)))) ENCARG(cons_from(cons_cons(0, x1))) -> c4(FROM(cons(0, encArg(x1))), ENCARG(cons_cons(0, x1))) ENCARG(cons_from(cons_cons(nil, x1))) -> c4(FROM(cons(nil, encArg(x1))), ENCARG(cons_cons(nil, x1))) ENCARG(cons_from(cons_cons(cons_active(z0), x1))) -> c4(FROM(cons(active(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_active(z0), x1))) ENCARG(cons_from(cons_cons(cons_mark(z0), x1))) -> c4(FROM(cons(mark(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_mark(z0), x1))) ENCARG(cons_from(cons_cons(cons_from(z0), x1))) -> c4(FROM(cons(from(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_from(z0), x1))) ENCARG(cons_from(cons_cons(cons_cons(z0, z1), x1))) -> c4(FROM(cons(cons(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_cons(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_s(z0), x1))) -> c4(FROM(cons(s(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_s(z0), x1))) ENCARG(cons_from(cons_cons(cons_head(z0), x1))) -> c4(FROM(cons(head(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_head(z0), x1))) ENCARG(cons_from(cons_cons(cons_2nd(z0), x1))) -> c4(FROM(cons(2nd(encArg(z0)), encArg(x1))), ENCARG(cons_cons(cons_2nd(z0), x1))) ENCARG(cons_from(cons_cons(cons_take(z0, z1), x1))) -> c4(FROM(cons(take(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_take(z0, z1), x1))) ENCARG(cons_from(cons_cons(cons_sel(z0, z1), x1))) -> c4(FROM(cons(sel(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_cons(cons_sel(z0, z1), x1))) ENCARG(cons_from(cons_s(cons_active(z0)))) -> c4(FROM(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_from(cons_s(cons_mark(z0)))) -> c4(FROM(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_from(cons_s(cons_from(z0)))) -> c4(FROM(s(from(encArg(z0)))), ENCARG(cons_s(cons_from(z0)))) ENCARG(cons_from(cons_s(cons_cons(z0, z1)))) -> c4(FROM(s(cons(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_cons(z0, z1)))) ENCARG(cons_from(cons_s(cons_s(z0)))) -> c4(FROM(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_from(cons_s(cons_head(z0)))) -> c4(FROM(s(head(encArg(z0)))), ENCARG(cons_s(cons_head(z0)))) ENCARG(cons_from(cons_s(cons_2nd(z0)))) -> c4(FROM(s(2nd(encArg(z0)))), ENCARG(cons_s(cons_2nd(z0)))) ENCARG(cons_from(cons_s(cons_take(z0, z1)))) -> c4(FROM(s(take(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_take(z0, z1)))) ENCARG(cons_from(cons_s(cons_sel(z0, z1)))) -> c4(FROM(s(sel(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_sel(z0, z1)))) S tuples: ACTIVE(head(cons(z0, z1))) -> c23(MARK(z0)) ACTIVE(2nd(cons(z0, z1))) -> c24(MARK(head(z1)), HEAD(z1)) ACTIVE(take(0, z0)) -> c25(MARK(nil)) ACTIVE(take(s(z0), cons(z1, z2))) -> c26(MARK(cons(z1, take(z0, z2))), CONS(z1, take(z0, z2)), TAKE(z0, z2)) ACTIVE(sel(0, cons(z0, z1))) -> c27(MARK(z0)) ACTIVE(sel(s(z0), cons(z1, z2))) -> c28(MARK(sel(z0, z2)), SEL(z0, z2)) FROM(mark(z0)) -> c38(FROM(z0)) FROM(active(z0)) -> c39(FROM(z0)) CONS(mark(z0), z1) -> c40(CONS(z0, z1)) CONS(z0, mark(z1)) -> c41(CONS(z0, z1)) CONS(active(z0), z1) -> c42(CONS(z0, z1)) CONS(z0, active(z1)) -> c43(CONS(z0, z1)) S(mark(z0)) -> c44(S(z0)) S(active(z0)) -> c45(S(z0)) HEAD(mark(z0)) -> c46(HEAD(z0)) HEAD(active(z0)) -> c47(HEAD(z0)) 2ND(mark(z0)) -> c48(2ND(z0)) 2ND(active(z0)) -> c49(2ND(z0)) TAKE(mark(z0), z1) -> c50(TAKE(z0, z1)) TAKE(z0, mark(z1)) -> c51(TAKE(z0, z1)) TAKE(active(z0), z1) -> c52(TAKE(z0, z1)) TAKE(z0, active(z1)) -> c53(TAKE(z0, z1)) SEL(mark(z0), z1) -> c54(SEL(z0, z1)) SEL(z0, mark(z1)) -> c55(SEL(z0, z1)) SEL(active(z0), z1) -> c56(SEL(z0, z1)) SEL(z0, active(z1)) -> c57(SEL(z0, z1)) ACTIVE(from(z0)) -> c22(MARK(cons(z0, from(s(z0)))), S(z0)) MARK(0) -> c35 MARK(nil) -> c36 MARK(from(z0)) -> c29(ACTIVE(from(z0)), FROM(mark(z0)), MARK(z0)) MARK(from(from(z0))) -> c29(ACTIVE(from(active(from(mark(z0))))), FROM(mark(from(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c29(ACTIVE(from(active(cons(mark(z0), z1)))), FROM(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c29(ACTIVE(from(active(s(mark(z0))))), FROM(mark(s(z0))), MARK(s(z0))) MARK(from(head(z0))) -> c29(ACTIVE(from(active(head(mark(z0))))), FROM(mark(head(z0))), MARK(head(z0))) MARK(from(2nd(z0))) -> c29(ACTIVE(from(active(2nd(mark(z0))))), FROM(mark(2nd(z0))), MARK(2nd(z0))) MARK(from(take(z0, z1))) -> c29(ACTIVE(from(active(take(mark(z0), mark(z1))))), FROM(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(from(0)) -> c29(ACTIVE(from(active(0))), FROM(mark(0)), MARK(0)) MARK(from(nil)) -> c29(ACTIVE(from(active(nil))), FROM(mark(nil)), MARK(nil)) MARK(from(sel(z0, z1))) -> c29(ACTIVE(from(active(sel(mark(z0), mark(z1))))), FROM(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(cons(from(z0), x1)) -> c30(ACTIVE(cons(active(from(mark(z0))), x1)), CONS(mark(from(z0)), x1), MARK(from(z0))) MARK(cons(cons(z0, z1), x1)) -> c30(ACTIVE(cons(active(cons(mark(z0), z1)), x1)), CONS(mark(cons(z0, z1)), x1), MARK(cons(z0, z1))) MARK(cons(s(z0), x1)) -> c30(ACTIVE(cons(active(s(mark(z0))), x1)), CONS(mark(s(z0)), x1), MARK(s(z0))) MARK(cons(head(z0), x1)) -> c30(ACTIVE(cons(active(head(mark(z0))), x1)), CONS(mark(head(z0)), x1), MARK(head(z0))) MARK(cons(2nd(z0), x1)) -> c30(ACTIVE(cons(active(2nd(mark(z0))), x1)), CONS(mark(2nd(z0)), x1), MARK(2nd(z0))) MARK(cons(take(z0, z1), x1)) -> c30(ACTIVE(cons(active(take(mark(z0), mark(z1))), x1)), CONS(mark(take(z0, z1)), x1), MARK(take(z0, z1))) MARK(cons(0, x1)) -> c30(ACTIVE(cons(active(0), x1)), CONS(mark(0), x1), MARK(0)) MARK(cons(nil, x1)) -> c30(ACTIVE(cons(active(nil), x1)), CONS(mark(nil), x1), MARK(nil)) MARK(cons(sel(z0, z1), x1)) -> c30(ACTIVE(cons(active(sel(mark(z0), mark(z1))), x1)), CONS(mark(sel(z0, z1)), x1), MARK(sel(z0, z1))) MARK(cons(x0, x1)) -> c30(CONS(mark(x0), x1)) MARK(cons(z0, z1)) -> c30(CONS(mark(z0), z1), MARK(z0)) MARK(s(from(z0))) -> c31(ACTIVE(s(active(from(mark(z0))))), S(mark(from(z0))), MARK(from(z0))) MARK(s(cons(z0, z1))) -> c31(ACTIVE(s(active(cons(mark(z0), z1)))), S(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(head(z0))) -> c31(ACTIVE(s(active(head(mark(z0))))), S(mark(head(z0))), MARK(head(z0))) MARK(s(2nd(z0))) -> c31(ACTIVE(s(active(2nd(mark(z0))))), S(mark(2nd(z0))), MARK(2nd(z0))) MARK(s(take(z0, z1))) -> c31(ACTIVE(s(active(take(mark(z0), mark(z1))))), S(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(nil)) -> c31(ACTIVE(s(active(nil))), S(mark(nil)), MARK(nil)) MARK(s(sel(z0, z1))) -> c31(ACTIVE(s(active(sel(mark(z0), mark(z1))))), S(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(head(z0)) -> c32(ACTIVE(head(z0)), HEAD(mark(z0)), MARK(z0)) MARK(head(from(z0))) -> c32(ACTIVE(head(active(from(mark(z0))))), HEAD(mark(from(z0))), MARK(from(z0))) MARK(head(cons(z0, z1))) -> c32(ACTIVE(head(active(cons(mark(z0), z1)))), HEAD(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(head(s(z0))) -> c32(ACTIVE(head(active(s(mark(z0))))), HEAD(mark(s(z0))), MARK(s(z0))) MARK(head(head(z0))) -> c32(ACTIVE(head(active(head(mark(z0))))), HEAD(mark(head(z0))), MARK(head(z0))) MARK(head(2nd(z0))) -> c32(ACTIVE(head(active(2nd(mark(z0))))), HEAD(mark(2nd(z0))), MARK(2nd(z0))) MARK(head(take(z0, z1))) -> c32(ACTIVE(head(active(take(mark(z0), mark(z1))))), HEAD(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(head(0)) -> c32(ACTIVE(head(active(0))), HEAD(mark(0)), MARK(0)) MARK(head(nil)) -> c32(ACTIVE(head(active(nil))), HEAD(mark(nil)), MARK(nil)) MARK(head(sel(z0, z1))) -> c32(ACTIVE(head(active(sel(mark(z0), mark(z1))))), HEAD(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(2nd(z0)) -> c33(ACTIVE(2nd(z0)), 2ND(mark(z0)), MARK(z0)) MARK(2nd(from(z0))) -> c33(ACTIVE(2nd(active(from(mark(z0))))), 2ND(mark(from(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c33(ACTIVE(2nd(active(cons(mark(z0), z1)))), 2ND(mark(cons(z0, z1))), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c33(ACTIVE(2nd(active(s(mark(z0))))), 2ND(mark(s(z0))), MARK(s(z0))) MARK(2nd(head(z0))) -> c33(ACTIVE(2nd(active(head(mark(z0))))), 2ND(mark(head(z0))), MARK(head(z0))) MARK(2nd(2nd(z0))) -> c33(ACTIVE(2nd(active(2nd(mark(z0))))), 2ND(mark(2nd(z0))), MARK(2nd(z0))) MARK(2nd(take(z0, z1))) -> c33(ACTIVE(2nd(active(take(mark(z0), mark(z1))))), 2ND(mark(take(z0, z1))), MARK(take(z0, z1))) MARK(2nd(0)) -> c33(ACTIVE(2nd(active(0))), 2ND(mark(0)), MARK(0)) MARK(2nd(nil)) -> c33(ACTIVE(2nd(active(nil))), 2ND(mark(nil)), MARK(nil)) MARK(2nd(sel(z0, z1))) -> c33(ACTIVE(2nd(active(sel(mark(z0), mark(z1))))), 2ND(mark(sel(z0, z1))), MARK(sel(z0, z1))) MARK(take(z0, x1)) -> c34(ACTIVE(take(z0, mark(x1))), TAKE(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(take(x0, z1)) -> c34(ACTIVE(take(mark(x0), z1)), TAKE(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(take(x0, from(z0))) -> c34(ACTIVE(take(mark(x0), active(from(mark(z0))))), TAKE(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(take(x0, cons(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(cons(mark(z0), z1)))), TAKE(mark(x0), mark(cons(z0, z1))), MARK(x0), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c34(ACTIVE(take(mark(x0), active(s(mark(z0))))), TAKE(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(take(x0, head(z0))) -> c34(ACTIVE(take(mark(x0), active(head(mark(z0))))), TAKE(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(take(x0, 2nd(z0))) -> c34(ACTIVE(take(mark(x0), active(2nd(mark(z0))))), TAKE(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(take(x0, take(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(take(mark(z0), mark(z1))))), TAKE(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(take(x0, 0)) -> c34(ACTIVE(take(mark(x0), active(0))), TAKE(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(take(x0, nil)) -> c34(ACTIVE(take(mark(x0), active(nil))), TAKE(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(take(x0, sel(z0, z1))) -> c34(ACTIVE(take(mark(x0), active(sel(mark(z0), mark(z1))))), TAKE(mark(x0), mark(sel(z0, z1))), MARK(x0), MARK(sel(z0, z1))) MARK(take(from(z0), x1)) -> c34(ACTIVE(take(active(from(mark(z0))), mark(x1))), TAKE(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c34(ACTIVE(take(active(cons(mark(z0), z1)), mark(x1))), TAKE(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(take(s(z0), x1)) -> c34(ACTIVE(take(active(s(mark(z0))), mark(x1))), TAKE(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(take(head(z0), x1)) -> c34(ACTIVE(take(active(head(mark(z0))), mark(x1))), TAKE(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(take(2nd(z0), x1)) -> c34(ACTIVE(take(active(2nd(mark(z0))), mark(x1))), TAKE(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c34(ACTIVE(take(active(take(mark(z0), mark(z1))), mark(x1))), TAKE(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(take(0, x1)) -> c34(ACTIVE(take(active(0), mark(x1))), TAKE(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(take(nil, x1)) -> c34(ACTIVE(take(active(nil), mark(x1))), TAKE(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(take(sel(z0, z1), x1)) -> c34(ACTIVE(take(active(sel(mark(z0), mark(z1))), mark(x1))), TAKE(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) MARK(sel(z0, x1)) -> c37(ACTIVE(sel(z0, mark(x1))), SEL(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(sel(x0, z1)) -> c37(ACTIVE(sel(mark(x0), z1)), SEL(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(sel(x0, from(z0))) -> c37(ACTIVE(sel(mark(x0), active(from(mark(z0))))), SEL(mark(x0), mark(from(z0))), MARK(x0), MARK(from(z0))) MARK(sel(x0, cons(z0, z1))) -> c37(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, s(z0))) -> c37(ACTIVE(sel(mark(x0), active(s(mark(z0))))), SEL(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(sel(x0, head(z0))) -> c37(ACTIVE(sel(mark(x0), active(head(mark(z0))))), SEL(mark(x0), mark(head(z0))), MARK(x0), MARK(head(z0))) MARK(sel(x0, 2nd(z0))) -> c37(ACTIVE(sel(mark(x0), active(2nd(mark(z0))))), SEL(mark(x0), mark(2nd(z0))), MARK(x0), MARK(2nd(z0))) MARK(sel(x0, take(z0, z1))) -> c37(ACTIVE(sel(mark(x0), active(take(mark(z0), mark(z1))))), SEL(mark(x0), mark(take(z0, z1))), MARK(x0), MARK(take(z0, z1))) MARK(sel(x0, 0)) -> c37(ACTIVE(sel(mark(x0), active(0))), SEL(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(sel(x0, nil)) -> c37(ACTIVE(sel(mark(x0), active(nil))), SEL(mark(x0), mark(nil)), MARK(x0), MARK(nil)) MARK(sel(x0, sel(z0, z1))) -> c37(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(from(z0), x1)) -> c37(ACTIVE(sel(active(from(mark(z0))), mark(x1))), SEL(mark(from(z0)), mark(x1)), MARK(from(z0)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c37(ACTIVE(sel(active(cons(mark(z0), z1)), mark(x1))), SEL(mark(cons(z0, z1)), mark(x1)), MARK(cons(z0, z1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c37(ACTIVE(sel(active(s(mark(z0))), mark(x1))), SEL(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(sel(head(z0), x1)) -> c37(ACTIVE(sel(active(head(mark(z0))), mark(x1))), SEL(mark(head(z0)), mark(x1)), MARK(head(z0)), MARK(x1)) MARK(sel(2nd(z0), x1)) -> c37(ACTIVE(sel(active(2nd(mark(z0))), mark(x1))), SEL(mark(2nd(z0)), mark(x1)), MARK(2nd(z0)), MARK(x1)) MARK(sel(take(z0, z1), x1)) -> c37(ACTIVE(sel(active(take(mark(z0), mark(z1))), mark(x1))), SEL(mark(take(z0, z1)), mark(x1)), MARK(take(z0, z1)), MARK(x1)) MARK(sel(0, x1)) -> c37(ACTIVE(sel(active(0), mark(x1))), SEL(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(sel(nil, x1)) -> c37(ACTIVE(sel(active(nil), mark(x1))), SEL(mark(nil), mark(x1)), MARK(nil), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c37(ACTIVE(sel(active(sel(mark(z0), mark(z1))), mark(x1))), SEL(mark(sel(z0, z1)), mark(x1)), MARK(sel(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, from_1, cons_2, s_1, head_1, 2nd_1, take_2, sel_2 Defined Pair Symbols: ACTIVE_1, FROM_1, CONS_2, S_1, HEAD_1, 2ND_1, TAKE_2, SEL_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_FROM_1, ENCODE_MARK_1, ENCODE_CONS_2, ENCODE_S_1, ENCODE_HEAD_1, ENCODE_2ND_1, ENCODE_TAKE_2, ENCODE_SEL_2 Compound Symbols: c23_1, c24_2, c25_1, c26_3, c27_1, c28_2, 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, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c22_2, c35, c36, c2_2, c3_2, c3_1, c4_2, c5_3, c5_2, c6_2, c7_2, c8_2, c9_3, c9_2, c10_3, c10_2, c29_3, c30_3, c30_1, c30_2, c31_3, c31_2, c32_3, c33_3, c34_4, c37_4, c_1, c1_1, c11_1